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EMPOWERgmatRichC
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If a is the sum of x consecutive positive integers. b is the 28 Jul 2019, 12:16
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Hi nvdmurty,

Based on the pattern that you're looking at, the goal wasn't to eliminate answer choices (as that information does not completely address Answers B, C or E). The pattern proves how D can never yield an equal result, since 'A" would be ODD and "B" would be EVEN.

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If a is the sum of x consecutive positive integers. b is the 17 Sep 2019, 22:32
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can be solved really quickly once you think of properties of sum of consecutives.
A. x-->Odd sum, y-->Odd sum can be
B. x--> E/O sum, y--> O sum can be
C. x--> E/O sum, y-->E/O sum can be
D. x--> O sum, y--> E sum cannot be!
E. x--> O sum, y--> E/O sum can be
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If a is the sum of x consecutive positive integers. b is the 04 Oct 2020, 04:42
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devinawilliam83
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
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this is a wrong question because first of all the first term of each X and Y consecutive positive integers isn't given. lets assume that the first term of both the set X and Y to be same then a will be equal to b only when X = Y

if the first terms are different than we can check any of the option for certainty only when both the first terms are known
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If a is the sum of x consecutive positive integers. b is the 04 Oct 2020, 22:47
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chikki420
devinawilliam83
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 wrong question because first of all the first term of each X and Y consecutive positive integers isn't given. lets assume that the first term of both the set X and Y to be same then a will be equal to b only when X = Y

if the first terms are different than we can check any of the option for certainty only when both the first terms are known
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Hi chikki420,

We're told that A is the sum of X CONSECUTIVE positive integers and B is the sum of Y CONSECUTIVE positive integers. We're asked for which of the following values of X and Y is it IMPOSSIBLE that A = B. This question is based on a subtle Number Property rule (and if you know the rule, then the question becomes a whole lot easier to deal with - and even if you don't know it, then you can figure out it with a little bit or Arithmetic). You can certainly TEST THE ANSWERS to prove what's possible and what's not (and I explain how in an earlier post in this thread), but I'm going to jump directly to what you've mentioned in your post.

This question is NOT asking us to prove which four options lead to equal sums; it's asking us for the one option in which equal sums can NEVER occur (and you do not actually need to know the starting values of each group to prove that).

Since we're dealing with CONSECUTIVE POSITIVE INTEGERS, some interesting patterns occur (based on the sum of those integers being either ODD or EVEN). Take a look at answer D....

X = 10 and Y = 4

The sum of 10 consecutive positive integers will ALWAYS be ODD... since there are 5 ODD numbers in that group (try it with any group of 10 consecutive positive integers and you'll see).
The sum of 4 consecutive positive integers will ALWAYS be EVEN... since there are 2 ODD numbers in that group (again, try it and you'll see)

An ODD number will NEVER equal an EVEN number.

So, A can NEVER EQUAL B in this circumstance, so this specific situation is the answer to this question.

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If a is the sum of x consecutive positive integers. b is the 05 Oct 2020, 13:02
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For consecutive integers:
Sum= n/2 (2a1+n-1), where a1 is the first term
Average = Median= Sum/n, where n= number of terms in the set
Value of average = median = either an integer (if n is odd) or integer+0.5 (if n is even)

Question stem is asking us to test all the choices and select the one where sum of one set cannot be equal to the sum of the other.
Simply put, Sum of one set cannot result into an average of either an integer (if n is odd) or (integer +0.5) (if n is even) on the other set.

For n=6, Sum S6 = 3(2a1+5)
For n=9, Sum S9 = 9/2 (2a1+8)= 9(a1+4)
For n=10, Sum S10 = 5(2a1+9)

A) For n=2, Median = S6 /2 = odd value /2= Integer.5, always
B) For n=3, Median = S6 /3 = multiple of 3 /3= Integer, always
C) For n=7, Median = S9 /7. Here, a1+4 /7= Integer when a1= (3+ multiples of 7)
D) For n=4, Median = S10 /4 = odd value /4= Integer.25. NOT POSSIBLE TO DERIVE Integer.5
E) For n=7, Median = S10 /7. Here, (2a1+9) /7= Integer when (2a1+9) is an (odd) multiple of 7.

Ans D
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If a is the sum of x consecutive positive integers. b is the 08 Nov 2022, 05:20
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Given: If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers.
Asked: For which of the following values of x and y is it impossible that a = b?

a = xs1 + x(x+1)/2
b = ys2 + y(y+1)/2

A. x = 2; y = 6
a = 2s1 + 3 ; b = 6s2 + 21; 2s1 + 3 = 6s2 + 21; 2s1 - 6s2 = 18; Possible
B. x = 3; y = 6
a = 3s1 + 6 ; b = 6s2 + 21; 3s1 + 6 = 6s2 + 21; 3s1 - 6s2 = 15; s1- 2s2 = 5; Possible
C. x = 7; y = 9
a = 7s1 + 28 ; b = 9s2 + 45; 7s1 + 28 = 9s2 + 45; 7s1 - 9s2 = 17; Possible
D. x = 10; y = 4
a = 10s1 + 55 ; b = 5s2 + 10; 10s1 + 55 = 4s2 + 10; 10s1 - 4s2 = -45; Impossible since 10s1 and 4s2 are even but 45 is odd
E. x = 10; y = 7
a = 10s1 + 55 ; b = 7s2 + 28; 10s1 + 55 = 7s2 + 28; 10s1 - 7s2 = -27; Possible


IMO D
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If a is the sum of x consecutive positive integers. b is the 01 Dec 2024, 00:55
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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.
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If a is the sum of x consecutive positive integers. b is the 04 Dec 2025, 14:53
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