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# If N/2 and M/5 are both integers, which of the following expressions m

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Joined: 02 Sep 2009
Posts: 53066
If N/2 and M/5 are both integers, which of the following expressions m  [#permalink]

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06 Feb 2019, 01:32
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Difficulty:

(N/A)

Question Stats:

89% (00:58) correct 11% (00:39) wrong based on 9 sessions

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If N/2 and M/5 are both integers, which of the following expressions must also be an integer?

A. $$\frac{N+M}{7}$$

B. $$\frac{NM}{7}$$

C. $$\frac{\frac{N}{2}+\frac{M}{5}}{2}$$

D. $$\frac{N+M}{10}$$

E. $$\frac{NM}{10}$$

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If N/2 and M/5 are both integers, which of the following expressions m  [#permalink]

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06 Feb 2019, 01:37
Bunuel wrote:
If N/2 and M/5 are both integers, which of the following expressions must also be an integer?

A. $$\frac{N+M}{7}$$

B. $$\frac{NM}{7}$$

C. $$\frac{\frac{N}{2}+\frac{M}{5}}{2}$$

D. $$\frac{N+M}{10}$$

E. $$\frac{NM}{10}$$

N = 2k

M = 5k

MN = 10 k

So , whenever we divide MN, it must be divisible by 10.

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Re: If N/2 and M/5 are both integers, which of the following expressions m  [#permalink]

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06 Feb 2019, 04:04
Bunuel wrote:
If N/2 and M/5 are both integers, which of the following expressions must also be an integer?

A. $$\frac{N+M}{7}$$

B. $$\frac{NM}{7}$$

C. $$\frac{\frac{N}{2}+\frac{M}{5}}{2}$$

D. $$\frac{N+M}{10}$$

E. $$\frac{NM}{10}$$

N = 2*a
M= 5*a
so
10* a*a
option E matches
IMO E
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Re: If N/2 and M/5 are both integers, which of the following expressions m   [#permalink] 06 Feb 2019, 04:04
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