If m - 4 is 7 more than n, then m + 9 is how much more than n + 2? : Problem Solving (PS)

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If m - 4 is 7 more than n, then m + 9 is how much more than n + 2?

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Math Expert

Joined: 02 Sep 2009

Posts: 52294

If m - 4 is 7 more than n, then m + 9 is how much more than n + 2? [#permalink]

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06 Feb 2017, 06:53

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If m - 4 is 7 more than n, then m + 9 is how much more than n + 2?

A. 5
B. 11
C. 13
D. 15
E. 18

Spoiler: OA

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Re: If m - 4 is 7 more than n, then m + 9 is how much more than n + 2? [#permalink]

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06 Feb 2017, 07:11

Bunuel wrote:

If m - 4 is 7 more than n, then m + 9 is how much more than n + 2?

A. 5
B. 11
C. 13
D. 15
E. 18

m-4 = 7+n

i.e. m = 11+n

m+9 = 20+n

i.e. m+9 = 18+(n+2)

Answer: Option E
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Re: If m - 4 is 7 more than n, then m + 9 is how much more than n + 2? [#permalink]

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06 Feb 2017, 13:51

If m - 4 is 7 more than n, then m + 9 is how much more than n + 2?

The above can be written as below
m - 4 = n + 7

Add 4 to both sides and you get
m = n + 2 + 5 + 4

Simplify the above
m = n + 2 + 9

Add 9 to both sides
m + 9 = n + 2 + 9 + 9

There m+9 is 18 more than n+2

Answer: E

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Re: If m - 4 is 7 more than n, then m + 9 is how much more than n + 2? [#permalink]

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08 Feb 2017, 14:16

GIVEN M-4 = 7+ N => M-N = 11 --(1)
Let x be the value by which N+2 WILL BE MORE THAN M+9
M+9 = x + (N+2) => M-N+7 =x --(2)
Substitute (1) in (2)
x = 11+7 = 18 (Ans E)

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Re: If m - 4 is 7 more than n, then m + 9 is how much more than n + 2? [#permalink]

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08 Feb 2017, 18:50

Bunuel wrote:

If m - 4 is 7 more than n, then m + 9 is how much more than n + 2?

A. 5
B. 11
C. 13
D. 15
E. 18

We are given that m - 4 is 7 more than n. Thus:

m - 4 = n + 7

m = n + 11

We need to determine how much more m + 9 is than n + 2, i.e., we need to determine the value of:

m + 9 - (n + 2) = ?

Since m = n + 11, we can substitute n + 11 for m in the above expression and we have:

n + 11 + 9 - (n + 2) = ?

n + 20 - n - 2 = 18

Answer: E
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