mdcash wrote:
devinawilliam83 wrote:
If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?
A. x = 2; y = 6
B. x = 3; y = 6
C. x = 7; y = 9
D. x = 10; y = 4
E. x = 10; y = 7
this is a very bad question ... no way a GMAT question... very time consuming ...
Actually, it isn't that bad. There is the logical approach of number properties that you can use but even if that doesn't work out in the limited time, go with brute force!
A. x = 2; y = 6
Sum of first 6 numbers is 6*7/2 = 21
Can the sum of two consecutive numbers be 21? Sure 10 and 11.
Out
B. x = 3; y = 6
Sum of first 6 numbers is 21. Can sum of three consecutive numbers be 21? Divide 21 by 3 to get 7. The three numbers will be 6, 7, 8.
Out
C. x = 7; y = 9
Sum of first 9 numbers is 9*10/2 = 45. Can sum of 7 consecutive numbers be 45? 45 is not divisible by 7 so this will not work. Try another method:
Sum1 = Sum2
7*Mean1 = 9*Mean2
If Mean1 = 9 and Mean2 = 7, it will satisfy. i.e. 6, 7, 8, 9, 10, 11, 12 and 3, 4, 5, 6, 7, 8, 9, 10, 11
Out
D. x = 10; y = 4
10*Mean1 = 4*Mean2
Mean1/Mean2 = 2/5
Both Mean1 and Mean2 must be fractions "something.5" (Even consecutive numbers)
Also, Mean1 = 2x and Mean2 = 5x
Hard. Hold it.
E. x = 10; y = 7
10*Mean1 = 7*Mean2
Mean1/Mean2 = 7/10
Mean1 must be a fraction "something.5" (10 consecutive numbers) and Mean2 must be an integer (7 consecutive numbers)
Such as 3.5/5 but you don't have 10 positive integers around 3.5
So perhaps 10.5/15
The numbers are
6, 7, 8, 9, 10, 11, 12, 13, 14, 15
and
12, 13, 14, 15, 16, 17, 18
Out
Answer (D) by elimination.
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Karishma
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