Last visit was: 13 Dec 2024, 14:28 It is currently 13 Dec 2024, 14:28
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Dec 2024
Posts: 97,874
Own Kudos:
685,612
 []
Given Kudos: 88,268
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,874
Kudos: 685,612
 []
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b the 17 Feb 2020, 05:17
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

64% (02:31) correct 36% (02:33) wrong based on 81 sessions

History

Date
Time
Result
Not Attempted Yet
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, then a − b =

(1) The values of both x and y lie between 120 and 130, not including the two.

(2) The difference between x and y equals two times the difference between a and b.


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
A
User avatar
BrentGMATPrepNow
User avatar
GMAT Club Legend
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,786
Own Kudos:
32,200
 []
Given Kudos: 799
Location: Canada
Expert reply
Posts: 6,786
Kudos: 32,200
 []
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b the 17 Feb 2020, 07:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, then a − b =

(1) The values of both x and y lie between 120 and 130, not including the two.

(2) The difference between x and y equals two times the difference between a and b.
Given: x = (2)(3)(7)(a), and y = (2)(2)(8)(b)

Target question: What is the value of a - b?

Statement 1: The values of both x and y lie between 120 and 130, not including the two.
x = (2)(3)(7)(a), which means x =42a, which means 120 < 42a < 130.
Since a is an INTEGER, we now know that a = 3
Also, y = (2)(2)(8)(b), which means y = 32b, which means 120 < 32b < 130
Since b is an INTEGER, we now know that b = 4
So, the answer to the target question is a - b = 3 - 4 = -1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The difference between x and y equals two times the difference between a and b.
In other words: x - y = 2(a - b)
Replace x and x to get: 42a - 32b = 2a - 2b
Rearrange to get: 40a = 30b
Divide both sides by 10 to get: 4a = 3b
At this point we can see that there are infinitely many values of a and b that satisfy the equation 4a = 3b. Here are two:
Case a: a = 3 and b = 4. In this case, the answer to the target question is a - b = 3 - 4 = -1
Case b: a = 6 and b = 8. In this case, the answer to the target question is a - b = 6 - 8 = -2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
avatar
righthand
avatar
Joined: 20 Jan 2020
Last visit: 13 Dec 2024
Posts: 31
Own Kudos:
225
Given Kudos: 66
Products:
GMAT Club Tests
Posts: 31
Kudos: 225
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b the 17 Feb 2020, 07:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x = 42a ; y =32b

s1: given a, b positive intergers & x,y both are between 120 to 130 ---> x & y can be worked out ---> a-b can also be.
hence, sufficient.

s2: x-y = 2(a-b) ---> will give relation between a & b.. not the differnence. not sufficient.

Answer:A
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 13 Dec 2024
Posts: 4,126
Own Kudos:
9,918
 []
Given Kudos: 97
 Q51  V47
Expert reply
Posts: 4,126
Kudos: 9,918
 []
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b the 17 Feb 2020, 08:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, then a − b =

(1) The values of both x and y lie between 120 and 130, not including the two.

(2) The difference between x and y equals two times the difference between a and b.

We know x is a multiple of 42, and y is a multiple of 32. There will only be one possible value of x between 120 and 130, and only one possible value of y, so using Statement 1 we can work out exactly what x and y are, and thus find a and b and answer the question.

From Statement 2, we know

(2)(3)(7)(a) - (2)(2)(8)(b) = 2(a - b)
42a - 32b = 2a - 2b
40a = 30b
a/b = 3/4

So Statement 2 simply gives us the ratio of a to b. It's possible that a = 3 and b = 4 (those are the values you find using Statement 1 alone), and a - b = -1. Or it's possible that a = 6 and b = 8, and then a - b = -2, for example. So Statement 2 is not sufficient, and the answer is A.

The wording of Statement 2 is a bit ambiguous though, since it's not clear if it means to describe a-b (which turns out to be negative), or the positive difference |a - b|. I don't think I've ever seen that situation in a real GMAT question (and I'd be surprised if I did).
Moderator:
Bunuel
Math Expert
97874 posts