Exactly how many bonds does Bob have?

(1) Of Bob’s bonds, exactly $21$ are worth at least $5,000 each
(2) Of Bob’s bonds, exactly $65$ percent are worth less than $5,000 each

Answer Choices

Correct answer marked below

Statement (1) ALONE is sufficient

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

Correct

EACH statement ALONE is sufficient

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

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Comments

GaisMay 21

Wait, why isn't (1) alone enough? It tells us 21 bonds are worth at least $5k... oh. because there could be way more bonds total that are worth less. got it, sneaky.

ZiggyMay 30

this is the classic "part vs whole" thing DS loves to test. anytime they give you a subset count you should be suspicious

SanjanaMay 30

ohhh that's why I got it wrong lol thanks

IsaacAug 1

can someone explain how the two statements link up? I see 65% are less than 5k so 35% are 5k or more, but where does the 21 come in?

RajuanAug 10

thank you!! the percent gives you the proportion and stmt 1 gives you the actual count. that's the whole trick

AniketMay 1

Is the answer C? Both together. Statement 2 by itself just gives a percentage with no actual number so it can't stand alone.

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Exactly how many bonds does Bob have?(1) Of Bob’s bonds, exactly 212121 are worth at least $5,000 each(2) Of Bob’s bonds, exactly 656565 percent are worth less than $5,000 each­