Last visit was: 11 Sep 2024, 20:22 It is currently 11 Sep 2024, 20:22
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Let a be the sum of x consecutive positive integers. Let b be the sum

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95451
Own Kudos [?]: 657763 [26]
Given Kudos: 87242
Send PM
CAT Tests Forum Quiz Mode
Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink] Let a be the sum of x consecutive positive integers. Let b be the sum   04 Mar 2022, 08:15
2
Kudos
24
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

42% (02:33) correct 58% (02:23) wrong based on 182 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
Let a be the sum of x consecutive positive integers. Let b be the sum of y consecutive positive integers. For which of the following values of x and y is it NOT possible that a =b?

(A) x = 2; y = 6
(B) x = 3; y = 6
(C) x = 6; y = 4
(D) x = 6; y = 7
(E) x = 7; y = 5


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Posts: 1124
Own Kudos [?]: 1124 [7]
Given Kudos: 629
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Send PM
Reviews Badge
Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink] Let a be the sum of x consecutive positive integers. Let b be the sum   04 Mar 2022, 14:02
5
Kudos
2
Bookmarks
Let's dive into option choices.

A. \(x = 2; y = 6\)
\(x = 2\); If I have two consecutive no.s one will be even and the other will be odd thus it's sum would be ODD.
\(y = 6\); I will have three odd no.s and three even no.s. Sum of 3 odds no.s is odd. Sum of 3 even no.s is even. Combined sum would be ODD. Thus, Thus \(a\) and \(b\) can be equal.

B. \(x = 3; y = 6\)
\(x = 3\) For three consecutive no.s two can be odd and can be even giving the sum EVEN OR it can be two even and one odd and thus the sum will be ODD. Both possibilities are there.
\(y = 6\) Same as first option. Sum will be ODD. Thus \(a\) and \(b\) can be equal.

C. \(x = 6; y = 4\)
x=6 Sum will be ODD. Refer above.
y = 4 For four consecutive no.s there will be 2 odd no.s and 2 even no.s. Thus the sum will be EVEN.
Here \(a \) and \(b\) can NOT be equal, and thus this is our answer.

You can similar check for other answer choices and eliminate then with the same logic used above.
General Discussion
User avatar
B
rajshreeasati
Manager
Manager
Joined: 11 Jul 2018
Posts: 72
Own Kudos [?]: 20 [0]
Given Kudos: 42
Send PM
Re: Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink] Let a be the sum of x consecutive positive integers. Let b be the sum   23 May 2022, 04:55
PyjamaScientist thanks for this approach. Its much more efficient than my approach. I used the more algebraic approach and then by taking the Sum in an AP sequence, but it took a lot of time.

Also, just a quick tip which I read in Kaplan- when going through options, start backwards from E to A. More often than not, the GMAT hides the Answer to "the following" type questions in these options. Majority of times, it turns out to be D or E.

Anyways, thanks! :)
User avatar
L
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Posts: 1124
Own Kudos [?]: 1124 [0]
Given Kudos: 629
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Send PM
Reviews Badge
Re: Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink] Let a be the sum of x consecutive positive integers. Let b be the sum   23 May 2022, 05:00
rajshreeasati
PyjamaScientist thanks for this approach. Its much more efficient than my approach. I used the more algebraic approach and then by taking the Sum in an AP sequence, but it took a lot of time.
Also, just a quick tip which I read in Kaplan- when going through options, start backwards from E to A. More often than not, the GMAT hides the Answer to "the following" type questions in these options. Majority of times, it turns out to be D or E.
Anyways, thanks! :)
Glad that you liked my solution. And thanks for your advice. Though my method is to start from choice (C) and then proceeding from there to other choices depending on the result I get from (C).
User avatar
B
RastogiSarthak99
Manager
Manager
Joined: 20 Mar 2019
Posts: 144
Own Kudos [?]: 16 [0]
Given Kudos: 282
Location: India
Send PM
GMAT ToolKit User
Re: Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink] Let a be the sum of x consecutive positive integers. Let b be the sum   19 Jun 2022, 15:53
Tough one! But not impossible. Here's how I thought of it:

a = sum of x consecutive POSITIVE integers; b = sum of y consecutive POSITIVE integers.

Honestly, I don't think this can be done in time without trial and error from the options. So, here we go:

x = 2; y = 6

x--> 1+2 = 3, 2+3 = 5, 3+4 = 7 (i'm noticing a difference of 2 between numbers, so the sequence is sort of like 3,5,7,9,.....)
y--> 1 + 2 + 3 + 4 + 5 + 6 = 21 (Do this with another and we see the sequence is 21,27,33....)

in Option A, x and y will match at 27-27. Hence Eliminated.

I tried the sme for option B, where I got 21-21 as same. Hence eliminated.

Option C is where I couldn't find a pair and therefore picked that. I didn't look at the other options because it may have taken time.

Bunuel any thoughts on this approach?
User avatar
B
Adarsh_24
Manager
Manager
Joined: 06 Jan 2024
Posts: 81
Own Kudos [?]: 8 [1]
Given Kudos: 241
Send PM
Re: Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink] Let a be the sum of x consecutive positive integers. Let b be the sum   29 Aug 2024, 04:58
1
Kudos
another method.

(A) x = 2; y = 6
assume x and x+1 & y, y+1, y+2, y+3, y+4, y+5
2x+1=6y+15
2(x-3y)=14
x-3y=14 possible

(B) x = 3; y = 6
3x+3=6y+15
x+1=2y+5
x-2y=4 possible

(C) x = 6; y = 4
6x+15=4y+6
9=2(2y-3x)
4.5=2y-3x
y and x integer => 2y and 3x integer. addition/ subtraction of integers can give integers only.
So wrong.
GMAT Club Bot
gmatclubot
Re: Let a be the sum of x consecutive positive integers. Let b be the sum [#permalink]
29 Aug 2024, 04:58
Moderator:
Bunuel
Math Expert
95451 posts