cleetus wrote:
Four friends have some coins. A has 2 less than B, who has 2 less than C. If D has 2 less than A and the product of the number of coins that each of them has is 5760, how many coins in all do they have among themselves?
A) 38
B) 40
C) 42
D) 46
E) 36
I think the above solutions are all pretty good but I figured it using another approach so I am writing it down.
Seeing that each friend has 2 less than another friend, I figured they are even consecutive integers (even because the product is even).
Then I thought the product is 5760 (which is 24 * 24 * 10 because 24^2 = 576)
Then I thought of the number which, to the power 4 is around 5760. because the required even numbers would be around this number.
10^4 = 10,000. So the number has to be less than 10, I said.
Next number I thought of was 8 since 8 = 2^3 and I know 2^12 = 4096 which is a little less than 5760.
Therefore, I suspected 6 * 8 * 10 * 12 will work out which I confirmed by cross checking with 24 * 24 * 10. Add them to get 36.
Some brute force, some logic but you get your answer in 30 secs.
_________________
Karishma
Veritas Prep GMAT Instructor
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