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Exactly how many bonds does Bob have?

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Exactly how many bonds does Bob have?  [#permalink]

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New post 27 Nov 2018, 07:02
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Difficulty:

  25% (medium)

Question Stats:

76% (00:44) correct 24% (01:18) wrong based on 58 sessions

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Project DS Butler: Day 22: Data Sufficiency (DS44)


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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

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Re: Exactly how many bonds does Bob have?  [#permalink]

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New post 27 Nov 2018, 08:19
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Top Contributor
gmatbusters wrote:

Project DS Butler: Day 22: Data Sufficiency (DS44)


For DS butler Questions Click Here


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


Target question: Exactly how many bonds does Bob have?

Statement 1: Of Bob’s bonds, exactly 21 are worth AT LEAST $5,000 each
We have no idea how many of Bob's bonds are worth LESS THAN $5000 each
Statement 1 is NOT SUFFICIENT

Statement 2: Of Bob’s bonds, exactly 65 percent are worth LESS THAN $5,000 each
There are infinitely many scenarios that satisfy statement 2. Here are two:
Case a: Bob as a total of 100 bonds, 65 of which are worth less than $5,000 each, and 35 of which are worth at least $5,000 each. In this case, the answer to the target question is Bob has 100 bonds
Case b: Bob as a total of 200 bonds, 130 of which are worth less than $5,000 each, and 70 of which are worth at least $5,000 each. In this case, the answer to the target question is Bob has 200 bonds
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that 65% of the bonds are worth less than $5,000 each, which also means 35% of the bonds are worth at least $5,000 each
Statement 1 tells us that 21 bonds are worth at least $5,000 each
Let T = the total number of bonds that Bob owns
So, we can write: 35% of T = 21
In other words, 0.35T = 21
Since we COULD solve this equation for T, we COULD answer the target question with certainty
As such, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Re: Exactly how many bonds does Bob have? &nbs [#permalink] 27 Nov 2018, 08:19
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Exactly how many bonds does Bob have?

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