Flashcards in Data Sufficiecy Deck (178)

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1

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1. In a certain year the United Nations total expenditures were $1.6billion. Of this amount, 67.8% was paid by the 6 highest contributing countries, and the balance was paid by the remaining 153 countries. Was country x among the 6 highest contributing countries?

1. 56 percent of the total expenditures was paid by the highest - contributing countries, each of which paid more than country x.

2. Country x paid 4.8 percent of the total expenditures

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SPOILER: E

Good post? |

United Nations= total expenditures $1.6billion

6 highest contributing countries = 67.8% i.e. av (11.30) per country i

153 countries = 32.2% i.e. (.2% per country)

Question = Was country x among the 6 highest contributing countries?

Using 1.

Top 5 Contributing nations = 56 percent of the total expenditures

Each paid more than x

If top countries paid - 56, we are not clear how many countries constitute the top that contributed 56%

There can be no relation that can be derived about the expenditure made by x

2) If country x paid = 4.8%

here 4.8% could constitute the top 6 or it can be the bottom 153.

Only if x constituted less than .2% then we could tell that it was part of bottom 153. else had it been greater than 12% or so, we could have made some definite reply

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If x,y and z are integers and xy + z is an odd integer, is x an even integer?

1. xy + xz is an even integer

2. y + xz is an odd integer

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SPOILER: A

xy + z is an odd integer

This means

CASE 1

xy is odd and z is even

x and y => odd

z=> even

CASE 2

xy is even and z is odd

either one of x and y is even or both of them are even

z=> odd

Ques=> Is x even?

Statement 1:

xy + xz is an even integer

If we take case 1

xy is odd

hence to make xy+xz even xz too should be odd

this cant be possible because z is even

now we consider case 2

xy is even

so in order to make xy+xz to be even .. xz too should be even

we know that z is odd

hence x has to be even

This statement is Sufficient

Statement 2

y + xz is an odd integer

for y+xz to be odd

i)

y is odd and

xz is even

let us take case 1 again

xy is odd and z is even

but this isnt possible because z is even

now lets look at case 2

xy is even and z is odd

y+xz is odd

y is odd

now if xy is even and y is odd

x has to be even

ii)

y is even

xz is odd

case 1

xy is odd and z is even

not possible becaouse z xz is odd

case 2

xy is even and z is odd

xz is odd

x has to be odd

looking at the conditions .. x could either be even or odd

Insufficient

Option

SPOILER: A

3

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xy + z is an odd integer

This means

CASE 1

xy is odd and z is even

x and y => odd

z=> even

CASE 2

xy is even and z is odd

either one of x and y is even or both of them are even

z=> odd

Ques=> Is x even?

Statement 1:

xy + xz is an even integer

If we take case 1

xy is odd

hence to make xy+xz even xz too should be odd

this cant be possible because z is even

now we consider case 2

xy is even

so in order to make xy+xz to be even .. xz too should be even

we know that z is odd

hence x has to be even

This statement is Sufficient

Statement 2

y + xz is an odd integer

for y+xz to be odd

i)

y is odd and

xz is even

let us take case 1 again

xy is odd and z is even

but this isnt possible because z is even

now lets look at case 2

xy is even and z is odd

y+xz is odd

y is odd

now if xy is even and y is odd

x has to be even

ii)

y is even

xz is odd

case 1

xy is odd and z is even

not possible becaouse z xz is odd

case 2

xy is even and z is odd

xz is odd

x has to be odd

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Option

SPOILER: A

Originally Posted by adt29

I did the problem this way.

Factored out 9^x. So we have the equation simplified to:

9^x (1+ 9^1 + 9^2 + 9^3 + 9^4 + 9^5) = y.

Since odd powers of 9 end in 9, the sum of ( 9^1 + 9^2 + 9^3 + 9^4 + 9^5 ) will end in 9. If you add a '1' to that, you get some number that ends in '0'.

Now if x=1/2 which is not an integer, 9^(1/2) = 3. And 3 times a number that ends in 0, will give you a number that is divisible by 5.

So doesn't statemtnet 2 get refuted? What am I missing here?

I didn;t get it. Why would you refute B.

You were right all through out.

(9^x) X (10y) = multiple of 10 only if

we can prove that 9^x will not result in a fraction or an irrational number.

Both A and B prove the statement therefore D is the right answer

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Of the 75 houses in a certaion community, 48 have a pation. How many of the houses in the community have a swimming pool?

1. 38 of the houses in the community have a pation but do not have a swimming pool

2. The number of houses in the community that have a patio and a swimming is equal to the number of houses in the community that have neither a swimming pool nor a patio.

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SPOILER: B

Total Number of Houses in the Community (T) = Houses with Patio (P) + Houses with Swimming Pool (S) - Houses with both (S and P) + Houses with (neither S and P)

T = P + S - (PxS) + !(P or S)

Statement 1)

38 houses have Patio but no S. Here the statement does not consider that there could be houses that may not have both a Patio and a Swimming Pool therefore Not Sufficient

Statement 2)

Suggests that Houses have both P and S = Houses having neither P or S.

Putting back in our equation above:

T = P + S - (PxS) + !(P or S)

(PxS) = ! (P or S)

Therefore T = P + S

T = 75

P = 38

S = 27

B is the right answer

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Q1. If x and y are positive integers, is xy a multiple of 8?

(1) GCD of x and y = 10

(2) LCM of x and y = 100

(folks, frustratingly enough , despite working quite a bit on number properties, I got this wrong...I know this is fairly basic but please post explanations)

SPOILER: Official Answer=C

Q2. Is 1/p > r/(r^2 + 2)?

(1) p = r

(2) r > 0

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SPOILER: Official Answer=C

Originally Posted by dominicsavio

Q1. Is 1/p > r/(r^2 + 2)?

(1) p = r

(2) r > 0

SPOILER: Official Answer=C

Statement 1:

If we replace p with r, the target question becomes "Is 1/r > r/(r^2 + 2)?"

In this form, it might be tough to answer the new target question.

However, since (r^2 + 2) must be positive, we can multiply both sides of the target question by (r^2 + 2) to get a new target question: Is (r^2 + 2)/r > r?

From here, we can simplify the left-hand-side to get Is r + 2/r > r?

Finally, if we subtract r from both sides of the target question, we get Is 2/r > 0?

At this point, it's easy to answer the target question.

2/r can be greater than zero or it can be less than zero.

As such, statement 1 is not sufficient.

Statement 2:

Since we are given no information about p, statement 2 is not sufficient.

Statements 1 AND 2:

Statement 1 allowed us to rewrite the question as Is 2/r > 0?

Since statement 2 tells us that r is positive, we can now answer the new target question with certainty (2/r is definitely greater than zero).

So, the answer is

SPOILER: C

Cheers,

Brent

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Q6:

a four sided figure abcd

In the figure shown, line segment AD is parallel to line segment BC. What is the value of x?

(1) y = 50

(2) z = 40

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Answer is D

Good post? |

IMO answer is A

AC is the traversal cutting the parallel lines BC and AD

1. Alternate angles y=x=50.Hence sufficient

2. z=40 but value of y is unknown.Even though we know the exterior angle theorem that angle= angle y+ angle z, we are still helpless as value of angle y is known to find value of angle x. hence insufficient.

So answer is A.

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The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are real GMAT scores but 412 and 765 are not). A first-year class at a certain business school consists of 478 students. Did any students of the same gender in the first-year class who were born in the same-named month have the same GMAT score?

(1) The range of GMAT scores in the first-year class is 600 to 780.

(2) 60% of the students in the first-year class are male.

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Given: If scores are between 200 and 800 then there are 60 scores possible. Assuming worst case, each kid is born in a different month so and different kids in the same month score different GMAT scores Therefore: 12*60 males and 12*60 ladies are possible720 males and 720 ladies can go without any repetition.

Option A If range = 600 - 780 then 18 scores possible. And the maximum again becomes 18*12= 216So if males = 217 and ladies = 217 then there has to be a repetitionIf total kids = 478 then minimum boys = 478/2 = 239 and so with ladies which is greater than 217 so it is sufficient

Option B Males = 227. Can't say. We need more than 712 of the same gender to prove the point so not sufficient

Official Answer please? imo = A

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Is 2x - 3y > x2 ?

(1) 2x - 3y = -2

(2) X >2 and y > 0

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SPOILER: Official Answer: D. i know its simple but took me more than few mins to get to it.. can anybody explain it better?

Nice question, Lav.

Target question: Is 2x - 3y > x2 ?

Statement 1: 2x - 3y = -2

Let's take the target question and replace 2x - 3y with -2

We get: Is -2 > x2 ?

The square of any number must be greater than or equal to zero, so we can be certain that -2 is not greater than x2 .

Since we can answer the target question with certainty, statement 1 is sufficient.

Statement 2: x >2 and y > 0

Let's first take the original target question (Is 2x - 3y > x2 ?) and subtract 2x from both sides

We get: Is -3y > x2 - 2x ?

Now factor the right hand side to get: Is -3y > x(x - 2) ?

Well since y>0, we know that -3y will be negative

Since x>2, we know that x(x-2) must be positive (since x-2 must be positive)

So, the target question is really asking Is some negative number > some positive number ?

We can answer this question with certainty (some negative number is not greater than some positive number)

Since we can answer the target question with certainty, statement 2 is sufficient.

So, the answer is

SPOILER: D

Cheers,

Brent

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At 9 a.m, a hiker was due south of point P. What direction was point P from her position at noon?

1. From 9 a.m to 11 a.m,she walked due east at 2 miles per hr, and from 11 a.m until noon, she walked due north at 3 miles per hr.

2. At noon, she is exactly 4.5 miles from point P.

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The answer is E.

At noon, we know:

a) the hiker is 4 miles east of point P

b) the hiker is 4.5 miles from point P

Unfortunately, we don't know whether the hiker is north or south of point P (so the answer is E, since the question asks us to find the direction from P)

Example:

- If the hiker is 1.5 miles south of point P at 9am, then at noon the hiker will be 1.5 miles north of P

- If the hiker is 4.5 miles south of point P at 9am, then at noon the hiker will be 1.5 miles south of P

In both cases, the hiker would be the same distance away from point P, but the direction would be different.

Cheers,

Brent

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If x > 1, what is the value ofinteger x?

(1) There are x unique factors of x.

(2) The sum of x and any prime number larger than x is odd.

The answer logic starts by mentioning that (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x.

Can some one explain (with example) what does it mean???

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Originally Posted by tarunlakhani

If x > 1, what is the value ofinteger x?

(1) There are x unique factors of x.

(2) The sum of x and any prime number larger than x is odd.

The answer logic starts by mentioning that (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x.

Can some one explain (with example) what does it mean???

Let's say that x=2.

Notice that 2 has 2 positive factors (divisors). They are 1 and 2

So, if x=2, we satisfy the condition that there are x unique factors of x.

Conversely, if x=3, the condition is not met.

Notice that 3 has only 2 positive factors. They are 1 and 3

Aside: the answer logic says "(1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x."

Given the present wording of the question, this is logic incorrect. The present wording allows for factors that are negative as well.

Now I'm assuming that the question is meant to restrict factors to positive factors, but this is not explicitly stated.

Okay, if we restrict x to being positive and we restrict the factors to being positive, statement 1 tells us that x must equal either 1 or 2. These are the only values where the number of positive factors equals the number itself.

I won't go any further, since the question, it its current form, has too many ambiguities.

Cheers,

Brent

Online video lessons | GMAT Prep Now

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If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.

(2) k is divisible by exactly 4 different prime numbers.

PLEASE EXPLAIN.

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Originally Posted by cinghal1

If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.

(2) k is divisible by exactly 4 different prime numbers.

PLEASE EXPLAIN.

(E) it is

(1) k is divisible by 4 => k can be a square of an interger (16, 64 ....) or not a square (12, 24 ...) => insuff

(2) k is divisible by exactly 4 different prime numbers. Again, k can be or not a square of an interger.

For example: Let's say k is divisible by 2, 3, 5, 7

If k = 210 = (2x3x5x7) => k is not a square

If k = 6300 = (2x2x3x3x5x5x7x7) => k is the square of 210

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In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) root a square + root b square = root c square + root d square

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SPOILER: Official Answer: C

Using distance formula we know that the given 2 points are equidistant from the origin when

: sqrt (a^2+b^2)=sqrt (c^2+d^2).

(Note that change in Xs and Ys for both points are actually the Xs and Ys of those points due to the fact that the question asks distance from “the origin”).

1/5=2/10 but if we square them we’ll get different answer. On the other hand 1/5= -1/-5 and these points are equidistant from the origin. INS.

By simplifying the equation we get: a+b=c+d, 2+4=1+5 but if we square each term then we see that 20 doesn’t equal 26. On the other hand 2+4=4+2 and the sum of their squares are equal.

INS.

For both statements let’s take poor mathematical approach, just for fun:

Question: a^2+b^2= c^2+d^2 if ad=bc and a+b=c+d?

a=c+d-b

((c+d)-b)^2+b^2= c^2+d^2

(c+d )^2-2b(c+d)+b^2+b^2= c^2+d^2

c^2+2cd+d^2-2bc-2bd+2b^2=c^2+d^2

2cd-2bc-2bd+2b^2=0

cd-bc-bd+b^2=0

-bc+b^2= bd- cd

b(b-c)=d(b-c)

b=d

If b=d we know that a=c (statement 2 (we cannot use statement 1 for that conclusion> if b and d equal 0 then a and c can equal any number)) and if two coordinates are equal it means that the points share the same coordinates and they are equidistant from the origin. SUFF C

13

## If a, b, and c are three consecutive prime numbers such that a

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from 1,

b=a+2=(a+b+c)/3

==> a+4=c

and we have a+2=b

the 3 primes are a,a+2,a+4

only 3,5,7 satisfies

2) suff.

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If x,y and z are integers and xy+z is an odd integer, is x an even integer?

1. xy and xz is an even integer

2. y + xz is an odd integer

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SPOILER: A

1 out of 1 members found this post helpful. Good post? |

from question stem, one of the xy & z is to be odd.

from stem 1, xy & xz = even. SO, xy must be even. so, z= odd (question stem).AS xz is even, X must be even. Sufficient. (B,C and E out)

from stem 2, one of xz or y is to be odd. let x=odd,y=odd and z=even. Question stem -(o*o+e = o) OK and stem 2, (o+o*e = o OK)

AGAIN, if x = e, y=o & z=o,question stem (e*o+o=o) and stem 2 (o+o*e = o). STILL OK. (D out)

A is the pick.

(under exam situation it will be a very tough question)

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Good post? |

Co-Ordinates

1. In the xy - co-ordinate plane, line L and line K intersect at point (4,3). Is the product of their slopes negative?

1. The product of the x-intercepts of the lines L and K is positive

2. The product of the y - intercepts of the lines L and K is negative

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SPOILER: C

The product of the slopes is negative, if one line is slanted “downwards” and the other one “upwards”.

Insufficient, try 1 and 6 (negative and positive slopes) and then try 6 and 6 (negative slopes) , 2 and 2 (positive slopes) , -5 and -2 (positive slopes).

Insufficient, try 1 and -1 (positive slopes), 4 and -6 (positive and negative slopes).

Both: The line which has negative y intercept, and one of its points lie in the first quadrant, must have positive x intercept and a positive slope .

The line which has positive y intercept and positive x intercept must have negative slope.

Thus the product of the slopes is negative. Suff. C

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What is the greatest common divisor of positive integers m and n?

1. m is a prime number

2. 2n = 7m

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Originally Posted by kjain

Brent, I feel that answer to first question should be E, because even by combining both conditions, I am unable to find GCD. Can you pls provide an explaination to this question.

Statement 1:

If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the GCD of m and n must be either 1 or m.

Since we know nothing about n, statement 1 is not sufficient.

Statement 2:

If 2n = 7m then we can rearrange the equation to get n = (7/2)m

Important aside: Notice that if m were to equal an odd number, then n would not be an integer. For example, if m=3, then n=21/2. Similarly, if m=11, then n=77/2. For n to be an integer, m must be even.

So, for example, we could have m=2 and n=7, in which case the GCD=1

We could also have m=4 and n=14, in which case the GCD=2

We could also have m=10 and n=35, in which case the GCD=5 . . . and so on.

Since we cannot determine the GCD with any certainty, statement 2 is not sufficient.

Statements 1 & 2

From statement 1, we know that m is prime, and from statement 2, we know that m is even.

Since 2 is the only even prime number, we can conclude that m must equal 2.

If m=2, then n must equal 7, which means that the GCD must be 1.

Since we are able to determine the GCD with certainty, statements 1 & 2 combined are sufficient, and the answer is

SPOILER: C

Cheers,

Brent

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Good post? |

DS - number properties

If r and s are positive integers, is r/s an integer?

a. Every factor of s is also a factor of r

b. Every prime factor of s is also a prime factor of r

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In my opinion A.

from a) if EVERY factor of s (denominator) is also factor of r (numerator), THEN r/s must be an integer.

let

s= 12 (factors, 1,2,3,4,6,12) r= 36(1,2,3,4,6,9,12,18,36)

Here EVERY factor of s (1,2,3,4,6,12) is also factor of r (1,2,3,4,6,9,12,18,36) . r/s = 36/12 = 3 (an integer). PLEASE NOTE: all the factors of r is not (9,18,36) factor of s, so if we devide s by r we will not get an integer. (12/36) = 0.33.

(sufficient)

from b) common prime factors can not ensure (as we dont know about their power) divisibility

let r = 6, S =12

Prime factorization of r= 2*3

Prime factorization of s=2^2 * 3

Here both r and s share s same prime factor (2,3) BUT r/s = 6/12 = 0.5 (not an integer)

let r=12, s=6, r/s= 12/6 = 2. (integer)

So we can not be sure. (not sufficient)

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If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

(1) k is parallel to the line with equation y = (1-m)x + b +1.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7)

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Originally Posted by missionGMAT

If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

(1) k is parallel to the line with equation y = (1-m)x + b +1.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7)

We know that if we write the equation of line in slope y-intercept form, y = mx + b, then m = the slope of the line and b = the y-intercept of the line.

The target question asks us to find the slope of line k, so we can reword the target question to be "What is the value of m?"

Statement 1:

We know that if 2 lines are parallel, their slopes must be equal.

So, the slope of line k is equal to the slope of the line with the equation y = (1-m)x + b +1

What is the slope of the line y = (1-m)x + b +1?

Well, since the equation y = (1-m)x + b +1 is written in slope y-intercept form, we can see that the slope of this line is 1-m

We also know that the slope of line k is m

Since the two lines are parallel, their slopes are equal, which means that 1-m = m

When we solve this equation, we get m = 1/2

Since we are able to find the value of m with certainty, statement 1 is sufficient.

Statement 2

All this really tells us is that line line k passes through the point (2,7).

Since there are a lot of different lines (with different slopes) that can pass through the point (2,7), there is no way to determine the slope of line k with any certainty.

As such, statement 2 is not sufficient, and the answer is A

Cheers,

Brent

19

## If 2^(-2k) =14. Along with -2 it gives a negative exponent ….if 2 is a prime, then k=14, if 3 is the first prime k=15. SUFFICIENT

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IMO B.

K>-2

1. K can be any odd number above -2. Insf

2. K-12 is prime and K >-2

K can have values 14, 15, 17, 23.....

Insuff

1 and 2 together....Still not suff, as 2 is the only even prime number....

20

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If n is a positive integer, is the value of b-a at least twice the value of 3^n-2^n?

1) a=2^(n+1) and b=3^(n+1)

2) n=3

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Good post? |

1) 3^n*3- 2^n*2 > 2*(3^n-2^n)?

3^n*3- 2^n*2-2*3^n+2*2^n >0?

3^n*3-2*3^n>0?

3^n>0?

answer is definitely yes

suff.

2) we don’t know values of b and a, thus ins

A

21

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Hi,

The question in Official Guide Ed.11 (128):

If x is an integer,is x|x|

###
Good post? |

1) Look at x as a negative scalar, more x moves left direction of the number line, the

“more negative” becomes xIxI, break even value for x=-2, when -2I-2I=2*(-2)

ins

2) Just plug in -10 (we already know that when x is negative, -2 is break even value and left hand side of inequality would be less than right hand side.

Suff

B

P.S. I don't get your question.

22

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If b, c, and d are constants and x2 + bx + c = (x + d)2 for all values of x, what is the value of c?

(1) d = 3

(2) b = 6

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Originally Posted by crazy800

Official Answer is D

I put it in the form

x^2 + bx + c = x^2 + 2dx+ d^2

i feel like i read somewhere in secondary level that in such cases, we can write in this form

c = d^2 and

bx = 2dx

if it works (1) is sufficient for sure because we get the value of d=6. as c = d^2, c = 6^2 = 36

but from (2), we can't find the value of 'd' or 'c'

No idea. Further explanation needed

You were right in the approach but I guess just missed for little

Taking thy approach furthur

x^2 + bx + c = x^2 + 2dx+ d^2

thus equating the coefficients of ax^2+bx + c we get

b = 2d -- eqn a

c = d^2 --- eqn b

from Option 1) d = 3

Thus c = 9 (from eqn b)

Sufficient

from 2) b = 6

Thus d = 3 (from eqn a)

and thus c = 9 (frm eqn b)

Sufficient

Hence D

23

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Please explain

If k, m, and t are positive integers and k/6+m/4=t/12 do t and 12 have a common factor greater than 1 ?

(1) k is a multiple of 3.

(2) m is a multiple of 3.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Good post? |

A

(2k+3m)/12=t/12

2k+3m=t

1) If k is a multiple of 3 we can factor out 3 from (2k+3m):

3(2*n+m)=t

note that 3n = k

So in any case t is multiple of 3

Suff

2) m is a multiple of 3

in this case we can or cannot factor out 3, depending on value of k.

e.g.

if k=1 and m=9

then t=29

if k= 3 and m=3

t=15 so shares multiples 1 and 3 with 12.

INS

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r s t

u v w

x y z

Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?

(1) v + z = 6

(2) s + t + u + x = 6

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

###
D

Good post? |

The question stem says that the value of a point 1,2 or 3. we can infer -

1. the highest value 3

2. the lowest value 1

3. sum of any row / column = 6.

from statement 1: v+z = 6. So, v=z=3. So, none of the alphabet in any row or column can be 3 ! R must be 3. Sufficient.

from statement 2:Column 1 + Row1 - 2r =12.

As per inference value (sum) of any column = 6. For the same reason value of any row = 6

Now, C1+R1 = 6+6 =12.

C1+R1 - 2r =6 => 2r=C1+R1 -6 => 2r = 12-6 => r =6/2 => r =3 . SUFFICIENT.

D is the pick

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If x and y are positive, is x3 > y?

(1) x^1/2 > y

(2) x > y

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

###
Good post? |

x can be between 0 and 1

thus E

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Is x less than y?

(1) x-y+1<0

The Official Answer given is A, which I think is wrong. Please comment.

###
Originally Posted by missionGMAT

Is x less than y?

(1) x-y+1< x+1 and x-1 < x

The target question asks "Is x < y?"

Statement 1: x-y+1< y

Since we also know that x < x+1, we can combine the two inequalities to get x < x+1 < y

From this we can see that x < y, so statement 1 is sufficient

Statement 2: x-y-1< y

Now we also know that x-1 < x, but what can we do with this?

We know that x and y are both greater than x-1, but we cannot say for certain whether or not y is greater than x.

As such, statement 2 is not sufficient and the answer is A

Cheers,

Brent

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For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?

The median equals the range

The largest number is twice the value of the smallest number

###
Originally Posted by missionGMAT

For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?

The median equals the range

The largest number is twice the value of the smallest number

Notice that if all 3 numbers are different, then we will have 3 different modes. So, if there is only 1 mode, then there are two possible cases:

case a: 2 numbers are equal and the 3rd number is different

case b: all 3 numbers are the same

Statement 1:

If the median equals the range, does the mode equal the range?

Well, does the median equal the mode here? The answer is yes. Here's why:

If we have case a, then the median must equal the mode (since it would be impossible for the middle-most number to be different from the other 2 values).

So, the median = mode = range

If we have case b, then the median must equal the mode, since all 3 numbers are equal.

So, the median = mode = range

Since we can be certain that the mode equals the range, statement 1 is sufficient.

Statement 2:

We can use counter-examples to show that this statement is not sufficient.

The 3 numbers could be 3, 3, 6 in which case the mode equals the range

The 3 numbers could be 3, 6, 6 in which case the mode does not equal the range

So, the answer is A

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A. Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?

1. The average (arithmetic mean) salary of the managers on the task force is $5000 less than the average salary of all employees on the task force

2. The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all the employees on the task force.

SPOILER: C

###
The DS wants to know whetehr the percentage of directors can be known.

let us consider

total employee (count) - x

director (count) - d

manager (count) - x-d

average salary of total employee = a

we have to find - d/x-d = ? or d/x = ? or d/ x-d = ?

from stem 1:

(x-d)(a+5000) = ...? we just have the connection between agerage salary of managers to average salay of all employee. as no other information is given to fill-up the right hand side of equation. we even can not go further. INSUFFICIENT. A, D OUT.

from stem 2:

d(a+15000) = .... ? the explanation is reciprocal for d (as per stem 1). B OUT.

LET US COMBINE -(x-d)(a-5000)+d(a+15000) = ax

=> xa - ad - 5000x - 5000d + ad + 15000d = ax

=> xa -ax - 5000 x + 15000d = 0

=> 5000x= 15000 d

=> x = (15000/5000)d

=>x/d =3 ( we got the ratio)

c is the pick.

alternatively, we can choose signs for average salaries of d,m.

Thus C is the answer.

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S is a set of integers such that

i) if a is in S, then –a is in S, and

ii) if each of a and b is in S, then ab is in S.

Is –4 in S?

(1) 1 is in S.

(2) 2 is in S.

###
Originally Posted by missionGMAT

S is a set of integers such that

i) if a is in S, then –a is in S, and

ii) if each of a and b is in S, then ab is in S.

Is –4 in S?

(1) 1 is in S.

(2) 2 is in S.

Statement 1:

All we can conclude is that 1 and -1 are in set S

INSUFF

Statement 2:

If 2 is in set S, then -2 is in set S (by rule i).

If 2 and -2 are in set S, then we can conclude is that -4 is in set S (by rule ii)

SUFF

So, the answer is B

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