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Senior RC Moderator V
Joined: 02 Nov 2016
Posts: 4106
GPA: 3.39
If 2 is the greatest number that will divide evenly into both x and y,  [#permalink]

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4 00:00

Difficulty:   5% (low)

Question Stats: 87% (00:46) correct 13% (01:02) wrong based on 76 sessions

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If 2 is the greatest number that will divide evenly into both x and y, what is the greatest number that will divide evenly into both 5x and 5y?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

Source: Nova GMAT
Difficulty Level: 500

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Re: If 2 is the greatest number that will divide evenly into both x and y,  [#permalink]

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1
Prime factorizing x,y will have at least one 2 in it.
Lets take values for x,y as 4(2^2),6(2*3)
If these values are multiplied by 5, they will be evenly divided by 5*2(Option E)
because the prime factorization will contain at least one 2 and one 5.

To double check use the assumed values of x(4) and y(6),
5*x is 20(2^2*5) and 5*y is 30(2*3*5).
Both these numbers are only divisible by 10(2*5)
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Re: If 2 is the greatest number that will divide evenly into both x and y,  [#permalink]

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If 2 is the greatest number that will divide evenly into both x and y, what is the greatest number that will divide evenly into both 5x and 5y?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

Source: GMAT for Dummies

2 is the greatest number that will divide evenly into both x and y
In other words, 2 is the greatest common divisor (GCD) of x and y.
Let's find 2 numbers that have a GCD of 2.
How about x = 2 and y = 2

What is the greatest number that will divide evenly into both 5x and 5y?
In other words, what is the greatest common divisor (GCD) of 5x and 5y.
If x = 2 and y = 2, then 5x = (5)(2) = 10, and 5y = (5)(2) = 10
The GCD of 10 and 10 is 10.

NOTE: this strategy works with every pair of values with a GCD of 2
For example x = 4 and y = 6
Here, 5x = (5)(4) = 20, and 5y = (5)(6) = 30, and the GCD of 20 and 30 is 10.

Cheers,
Brent
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Re: If 2 is the greatest number that will divide evenly into both x and y,  [#permalink]

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_________________ Re: If 2 is the greatest number that will divide evenly into both x and y,   [#permalink] 26 Mar 2019, 09:47
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