Consecutive integers problem

[rishianand7]

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

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Hi rishianand7,

This question is based on a subtle Number Property rule (and if you know the rule, then the question becomes a whole lot easier).

A = sum of x consecutive positive integers
B = sum of y consecutive positive integers

Under what circumstances can A NEVER EQUAL B?

You can certainly TEST numbers to prove what's possible and what's not:

If x = 2 and y = 6 you could have

A = 10 + 11 = 21
B = 1 + 2 + 3 + 4 + 5 + 6 = 21

In this example, A EQUALS B, so this is not the answer we're looking for.

If x = 3 and y = 6 you could have

A = 6 + 7 + 8 = 21
B = 1 + 2 + 3 + 4 + 5 + 6 = 21

In this example, A EQUALS B, so this is not the answer we're looking for.

You could continue with this method to figure out which of the other 3 answers are possible and which is not.

With this Number Property though, you'll be able to quickly solve this problem:

Take a look at answer D....

x = 10 and y = 4

The sum of 10 consecutive positive integers will always be ODD (try it and you'll see)
The sum of 4 consecutive positive integers will always be EVEN (again, try it and you'll see)

So, A can NEVER EQUAL B in this circumstance.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

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

Even integers and odd integers ALTERNATE.

A:
x = 2 = sum of 1 even and 1 odd = ODD.
y = 6 = sum of 3 evens and 3 odds = ODD.
Here, x and y both yield ODD sums.

B:
x = 3 = sum of 1 even and 2 odds = EVEN or sum of 2 evens and 1 odd = ODD.
y = 6 = sum of 3 evens and 3 odds = ODD.
Here, it is possible that x and y both yield ODD sums.

C:
x = 7 = sum of 3 evens and 4 odds = EVEN or sum of 4 evens and 3 odds = ODD.
y = 9 = sum of 4 evens and 5 odds = ODD or sum of 5 evens and 4 odds = EVEN.
Here, is is possible that x and y both yield EVEN sums or that x and y both yield ODD sums.

D:
x = 10 = sum of 5 evens and 5 odds = ODD.
y = 4 = sum of 2 evens and 2 odds = EVEN.
Here, it is NOT possible that x and y yield equal sums.

E:
x = 10 = sum of 5 evens and 5 odds = ODD.
y = 7 = sum of 3 evens and 4 odds = EVEN or sum of 4 evens and 3 odds = ODD.
Here, it is possible that x and y both yield ODD sums.

The correct answer is D.