Manhattan Question Set # 7

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Sun Oct 09, 2016 5:59 pm

In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y's sale price and cost per unit?

(A) $3
(B) $4
(C) $7
(D) $11
(E) $51

OA: D

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Source: Beat The GMAT — Problem Solving | Sun Oct 09, 2016 5:59 pm

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by [email protected] » Sun Oct 09, 2016 8:12 pm

Hi richachamption,

While this question is a bit wordy, it ultimately asks us to determine which of the 5 numbers COULD NOT be a divisor of 5304. Thus, we can either divide each answer into 5304 until we find the one that does not divide in evenly or we can 'prime-factor' 5304. Depending on your comfort level doing that type of division by hand, you might find one method faster than the other.

If you know your division rules though, then you can quickly eliminate Answers A and B. The digits in 5304 sum to 5+3+0+4 = 12, so this number IS divisible by 3. The last two digits of the number are 04, which is divisible by 4, so this number IS divisible by 4. So at this point, the question really comes down to how quickly you can divide in 1-2 of the remaining answers.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Oct 10, 2016 6:03 am

richachampion wrote:In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y's sale price and cost per unit?

(A) $3
(B) $4
(C) $7
(D) $11
(E) $51

Question rephrased: What was the amount of profit per unit?
Total profit over 7 days = 5304*7 = (2*3*4*13*17)*7.
This product is a multiple of every answer choice except for 11.
Thus, it is not possible that the profit per unit was $11.

The correct answer is D.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Oct 14, 2016 2:23 am

Let's say s = sale and c = cost. We've got

5304 * 7 = q * (s - c)

so assuming s and c are integers, which is a big assumption, we can streamline the process by saying that (s - c) is a factor of 5304 * 7. 5+3+0+4 = 12, so 3 is possible. 5304 ends in 04, so 4 is possible. 5304 * 7 divides by 7, so 7 is possible. 5304 = 5100 + 204 = 5100 + 51*4, so 51 is possible. That leaves us with 11.

(Alternatively, we could use the trick for divisibility by 11 to arrive at D, but this isn't a trick really worth learning for the GMAT.)

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