gmatbusters wrote:

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

For DS butler Questions Click HereExactly 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 eachThere 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 bondsCase 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 bondsSince 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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