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Interesting Q from test prep blog

This topic has 1 expert reply and 1 member reply

Interesting Q from test prep blog

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Nate Dogg sings hooks for two different prices: $52 for an EP and $58 for an LP. How many EP hooks did he sing?

(1) Nate sang a total of 9 hooks

(2) Nate earned $492 from singing hooks

This is the explanation of the answer:
Let’s see if it’s even possible for him to sing anything more than or less than 9. If he were to sing 8, to keep his profit at $492 while selling fewer items, he’d want to focus on more expensive items. And even the most expensive, $58, won’t net him enough for a total of 8: 8 x 58 = $464, which is not enough. Trying the same thing for 10, we find that even 10 of the least expensive items, $52, is too much: 10 x $52 = $520, and that’s too much. So, therefore, statement 2 guarantees statement 1 without our needing to be told so explicitly. Therefore, statement 2 is sufficient alone, and the correct answer is B.

I understand the below piece

"Let’s see if it’s even possible for him to sing anything more than or less than 9. If he were to sing 8, to keep his profit at $492 while selling fewer items, he’d want to focus on more expensive items. And even the most expensive, $58, won’t net him enough for a total of 8: 8 x 58 = $464, which is not enough. Trying the same thing for 10, we find that even 10 of the least expensive items, $52, is too much: 10 x $52 = $520, and that’s too much. So, therefore, statement 2 guarantees statement 1 without our needing to be told so explicitly."

But I don't get the one below:

Therefore, statement 2 is sufficient alone, and the correct answer is B.

How are we saying that B is sufficient without proving that it is sufficient. I answered it correctly by doing math and proving that B is right, but my approach (of doing math) on this kind of problems will definitely take more than 2 mins. But the blog's author's approach looks quite intuitive.

Can someone explain?


This is the original post:
http://www.beatthegmat.com/mba/2010/12/11/data-sufficiency-the-suge-knight-way

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From statement 1, we know that the total is 9 but individual hooks of EP and LP may be any integers having sum 9 i.e. x + y = 9, so Not Sufficient.

From statement 2, we know that 52*x + 58*y = 492 where x and y represent the number of EP and LP hooks respectively. Taking 2 as a common factor, we get 26*x + 29*y = 246.

As x and y can only take integer values, so y = (246 - 26*x)/29
From here you need to do some calculation as x takes values as 1,2,3,4....y must come out to be an integer and for y to be an integer, (246 - 26*x) must be divisible by 29. The only pair that satisfies the above is (x,y) = (5,4)

Hence unique solution...Sufficient

In DS you normally get these kind of questions so may need to do some extra bit of calculations rather than typical algebra.

So answer is B

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GMAT/MBA Expert

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achieve_dream wrote:
Nate Dogg sings hooks for two different prices: $52 for an EP and $58 for an LP. How many EP hooks did he sing?

(1) Nate sang a total of 9 hooks

(2) Nate earned $492 from singing hooks
Let E = the number of EP hooks and L = the number of LP hooks.

Statement 1: Nate sang a total of 9 hooks
Thus, E+L = 9.
No way to solve for E.
INSUFFICIENT.

Statement 2: Nate earned $492 from singing hooks
52E + 58L = 492.
If E+L = 8, the MAXIMUM amount that could be earned = 52*0 + 58*8 = 464. Too small.
If E+L = 10, the MINIMUM amount that could be earned = 52*10 + 58*0 = 520. Too great.
Thus, E+L = 9.
Two variables (E and L), two distinct linear equations (52E + 58L = 492, E+L = 9).
Thus, the value of E can be determined.
SUFFICIENT.

The correct answer is B.

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