Nate Dogg sings hooks for two different prices: $52 for an EP and $58

Question

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

anudeep133 · Answer

Solution:

Statement1 : There can be many combinations of EPs and LPs. So, insufficient.

Statement2 : Let no. of EP be x and total be n.
Then 52x + 58(n-x) = 492 ==> 58n - 6x = 492 ==> 3x = 29n - 246 ==> x = 29(n/3) - 82.
n=3,6 yield negative values for x. n=9 yields x=5. But n =12 or greater yields a value of x which will be greater than n which is not feasible for us.
So, n=9 and x=5.

Option, B

shailendra79s · Answer

No. of EP hooks = x
No. of LP hooks = y
From (1): x+y=9; Insufficient
From (2):
52x+58y=492 --> 26x+29y=246
-->x=(246-29y)/26
Since x & y can take only integer values, 
The value of x & y = (5,4); Sufficient
Answer: B

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

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 
 
Looking at the original condition, we can notice that this is a typical 2by2 question in GMAT test and the table is as below. 
 
There are 2 variables (a,b) and we need 2 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), C is likely the answer. Using both 1) & 2) together, a+b=9, 52a+56b=492 gives us b=4,a=5 and thus C is the answer. But hidden integer questions such as this question usually turns out to be common mistake type 4(A), thus we should try using the conditions separately. Using 1) and 2) separately, in case of 2) we have 52a+56b=492, 26a+29b=246 and since (26,29) is relative prime numbers (pair whose common factor is 1) a and b is a positive integer. Normally there is only 1 answer for the pair. Looking at 2), we have 26a+29b=246 and the answer is a=5, b=4, a unique answer. The condition is sufficient, therefore the answer is B. This is 5051 level question.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Clearly the answer is C, right? Each of statements 1 and 2 provides one equation, and we have two variables:

x + y = 9

52x + 58y = 492

But C comes a little too easy, and as Tupac also sang in I Get Around, “I don’t want it if it’s that easy.” Because the GMAT is likely trying to trap you with answer choice C, you need to push yourself to derive more value from one of the statements, as on a test this hard they won’t likely reward you so easily. As statement 2 seems to provide slightly more value than does statement 1, a helpful tip on a question like this is to use the more-robust statement to try to prove the other; in this case, does statement 2 guarantee that Nate sang 9 hooks?

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 .

What’s most important here is the takeaway – when either answer C or E comes to you too quickly, it’s almost certainly not correct. The GMAT will reward you for deriving more value from the statements than first meets the eye, and therefore your goal when you encounter an “Eazy E” or an easy C is to try to find the next answer up – use the information that you have to use just one statement alone (if you think C) or to find a way to solve the problem with both (if you initially think E).

bumpbot · Answer

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Nate Dogg sings hooks for two different prices: $52 for an EP and $58

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