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If x and y are integers, what is the least possible positive value of
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01 Jul 2021, 08:02
01 Jul 2021, 08:02
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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
A. 1
B. 3
C. 5
D. 7
E. 9
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x and y are integers, what is the least possible positive value of
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01 Jul 2021, 08:08
01 Jul 2021, 08:08
2
Carcass wrote:
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
A. 1
B. 3
C. 5
D. 7
E. 9
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
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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
gmatclubot
Re: If x and y are integers, what is the least possible positive value of [#permalink]
01 Jul 2021, 08:08
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