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kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
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Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
22 May 2019, 08:21
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A
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Difficulty:
45%
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68% (01:49) correct
32%
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based on 85
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The cost of each crate of milk is $40 and each crate of eggs is $25. If the seller sells at least one crate of each type every week and the number of crates sold is an integer find out how many crates of eggs did he sell last week?
I. Last week the seller sold eggs and milks worth $300.
II. The number of crates of eggs sold is one more than the number of crates of milk sold.
I. Last week the seller sold eggs and milks worth $300.
II. The number of crates of eggs sold is one more than the number of crates of milk sold.
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22 May 2019, 09:10
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Using Statement 1, if he sells m crates of milk and e crates of eggs, we have:
40m + 25e = 300
and dividing by 5 on both sides, we have
8m + 5e = 60
Two of the three numbers above are multiples of 5, so the third also must be (if it's not clear why that is true, we can rewrite the equation as 8m = 60 - 5e = 5(12 - e), and if 8m is equal to 5 times something else, 8m must be a multiple of 5). If 8m is a multiple of 5, then m is a multiple of 5, and since m > 0, the only possible value for m is 5, since if m were 10 or greater, the total cost of the crates would be too large. Since we can find m, we can find e, so Statement 1 is sufficient.
Statement 2 is clearly not sufficient, so the answer is A. Note though that there's a problem with Statement 2 -- it's not consistent with Statement 1. It should say that the number of crates of milk is one greater than the number of crates of eggs, not the reverse, which is what it says now.
40m + 25e = 300
and dividing by 5 on both sides, we have
8m + 5e = 60
Two of the three numbers above are multiples of 5, so the third also must be (if it's not clear why that is true, we can rewrite the equation as 8m = 60 - 5e = 5(12 - e), and if 8m is equal to 5 times something else, 8m must be a multiple of 5). If 8m is a multiple of 5, then m is a multiple of 5, and since m > 0, the only possible value for m is 5, since if m were 10 or greater, the total cost of the crates would be too large. Since we can find m, we can find e, so Statement 1 is sufficient.
Statement 2 is clearly not sufficient, so the answer is A. Note though that there's a problem with Statement 2 -- it's not consistent with Statement 1. It should say that the number of crates of milk is one greater than the number of crates of eggs, not the reverse, which is what it says now.
