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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Interesting Q from test prep blog ##### This topic has 1 expert reply and 1 member reply ## Interesting Q from test prep blog 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:
Letâ€™s see if itâ€™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, heâ€™d want to focus on more expensive items. And even the most expensive,$58, wonâ€™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 thatâ€™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

"Letâ€™s see if itâ€™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, heâ€™d want to focus on more expensive items. And even the most expensive,$58, wonâ€™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 thatâ€™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.

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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.

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