Flashcards in Manhatten Gmat Deck (4)

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Question

Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?
(1) The mean of Set A is greater than the median of Set B.
(2) The median of Set A is greater than the median of Set C.
(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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my answer is E

given: A = B + C

asking: medB > medA ?

(1) meanA > medB

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useless, the mean indicates nothing for finding medians

the mean can be easily misleading if one element is too large or too small

statement 1 is insufficient

(2) medA > medC

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although this could be a trap to make you think that the large medB cause medA > medC , the question says nothing about the number of elements in sets B and C. So, C could have like 10 elements while be has only 3 elements and thus the median of A could be larger than the median of B

on the other hand, B could have way more elements than C and thus resulting in a median of A smaller than the median of B

statement 2 is insufficient

(1) and (2) together

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is still not helpful as the mean in A leads to nothing

my answer is then E

OA ?

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Right angle triangle. ABC.

Angle abc is 90 degrees

Greg and Brian are both at Point A (above). Starting at the same time, Greg drives to point B while Brian drives to point C. Who arrives at his destination first?
(1) Greg's average speed is 2/3 that of Brian's.
(2) Brian's average speed is 20 miles per hour greater than Greg's.
(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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A

Mon Aug 08, 2011 12:16 pmThankQuote

I always enjoy going from A to B.

Keep in mind that the one who arrives first is the one who took less time.

If AB is x, then AC is x*root(2), since it is a 45-45-90 triangle.

If we draw a RTD chart here, before the statements:

Greg: Rg * Tg = x

Brian: Rb * Tb = x*root(2)

R = Rate, T = Time, g, = greg, b = brian

We want to compare Tg and Tb

Statement 1:

Greg: (2/3)Rb * Tg = x

Brian: Rb * Tb = x*root(2)

Tg = x / [2Rb/3] = x * [3/(2Rb)] = 3x/(2Rb)

Tb = x*root(2)/Rb

Tg = (x/Rb) * (3/2)

Tb = (x/Rb) * root(2)

Since 3/2 > root(2), Greg's time was longer, so Greg gets there later. Sufficient. Disappointing for me (Greg).

We cannot make the same conclusion using Statement 2. The speeds could be 21 and 1, in which case Brian would get there first easily because he goes so much faster. Or the speeds could be 9920 and 9900, in which case Greg would get there first easily because the speeds are very similar and Greg's distance is much less. Insufficient.

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In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?

a) 24

b) 52

c) 96

d) 144

e) 648

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This is a Manhattan GMAT question. OA is B.

It can be found on "Manhattan GMAT Archive (tough problems set).doc" and on http://www.manhattangmat.com/forums/gma ... -t886.html.

I don't like their answer; too Manhattan like = too wordy.

Here's my answer:

Scenario 1: g+s+b --> 4P3 = 4C3 3! = 24

Scenario 2: g+g+s --> 4C2 * 2C1 = 12

Scenario 3: g+s+s --> 4C2 * 2C1 = 12

Scenario 4: g+g+g --> 4C3 = 4

24+12+12+4=52

This answer assumes that the order of the runners receiving same medals, which is random, does not affect the positioning on the victory circle.

_________________

Please kudos if my post helps.

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