If x and y are integers, what is the least possible positive value of 21x + 35y?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Wed Mar 25, 2020 6:31 am

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If x and y are integers, what is the least possible positive value of 21x + 35y?

A. 1
B. 3
C. 5
D. 7
E. 9

Answer: D
Source: Math Revolution

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Re: If x and y are integers, what is the least possible positive value of 21x + 35y?

by Brent@GMATPrepNow » Wed Mar 25, 2020 9:21 am

BTGModeratorVI wrote: ↑
Wed Mar 25, 2020 6:31 am
If x and y are integers, what is the least possible positive value of 21x + 35y?

A. 1
B. 3
C. 5
D. 7
E. 9

Answer: D
Source: Math Revolution

21x + 35y = 7(3x + 5y)

Since x and y are INTEGERS, we know that 3x and 5y are each INTEGERS, which means 3x + 5y equals some integer
So, we can write: 21x + 35y = 7(some integer)
In other words, 21x + 35y is a multiple of 7

Check the answer choices.....only D is a multiple of 7

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: If x and y are integers, what is the least possible positive value of 21x + 35y?

by Brent@GMATPrepNow » Wed Mar 25, 2020 9:21 am

BTGModeratorVI wrote: ↑
Wed Mar 25, 2020 6:31 am
If x and y are integers, what is the least possible positive value of 21x + 35y?

A. 1
B. 3
C. 5
D. 7
E. 9

Answer: D
Source: Math Revolution

Another approach:

There's a nice rule that says:
If j, k and d are integers, and j is a multiple of d, and k is a multiple of d, then (j+k) must be a multiple of d

21x is a multiple of 7, since 21x = 7(3x)
35y is a multiple of 7, since 35y = 7(5y)

Since 21x and 35y are multiples of 7, the sum 21x + 35y must be a multiple of 7.
Since only 1 answer choice (D) is a multiple of 7, D must be the correct answer.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If x and y are integers, what is the least possible positive value of 21x + 35y?

by Scott@TargetTestPrep » Fri Mar 27, 2020 6:17 am

BTGModeratorVI wrote: ↑
Wed Mar 25, 2020 6:31 am
If x and y are integers, what is the least possible positive value of 21x + 35y?

A. 1
B. 3
C. 5
D. 7
E. 9

Answer: D
Source: Math Revolution

21x + 35y = 7(3x + 5y)

Since x and y are integers, we see that 7(3x + 5y) must be a multiple of 7. Since the only given answer choice that is a multiple of 7 is 7, choice D must be the correct answer.

Answer: D

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