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If seven times m is equivalent to both three times n and 2 times p, wh

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If seven times m is equivalent to both three times n and 2 times p, wh  [#permalink]

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02 Apr 2020, 01:41
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Difficulty:

55% (hard)

Question Stats:

65% (01:52) correct 35% (01:55) wrong based on 52 sessions

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If seven times m is equivalent to both three times n and 2 times p, what is the value of m + n + p?

(1) m – n = –4
(2) n + p = 5

Project DS Butler Data Sufficiency (DS3)

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Re: If seven times m is equivalent to both three times n and 2 times p, wh  [#permalink]

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02 Apr 2020, 02:27
1
Bunuel wrote:
If seven times m is equivalent to both three times n and 2 times p, what is the value of m + n + p?

(1) m – n = –4
(2) n + p = 5

Project DS Butler Data Sufficiency (DS3)

Give: 7m = 3n = 2p

Question: m+n+p = ?

Statement 1: m – n = –4

Substituting n = 7m/3 we get

m – 7m/3= –4
m = 3 i.e. values of n and p also may be obtained hence

SUFFICIENT

Statement 2:n + p = 5

Substituting n in terms of p gets us the unique value of
i.e. we can get unique values of m and p as well hence

SUFFICIENT

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Re: If seven times m is equivalent to both three times n and 2 times p, wh  [#permalink]

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02 Apr 2020, 03:35
1
Bunuel wrote:
If seven times m is equivalent to both three times n and 2 times p, what is the value of m + n + p?

(1) m – n = –4
(2) n + p = 5

Given, $$7m = 3n = 2p$$
Let $$7m = 3n = 2p = 42k$$ [LCM(7, 3, 2) = 42]
--> $$m = 6k; n = 14k; p = 21k$$
--> $$m + n + p = 6k + 14k + 21k = 41k$$

(1) $$m – n = –4$$
--> $$6k - 14k = -4$$
--> $$8k = 4$$
--> $$k = \frac{1}{2}$$
--> $$m + n + p = 41*\frac{1}{2}$$ --> Sufficient

(2) $$n + p = 5$$
--> $$14k + 21k = 5$$
--> $$35k = 5$$
--> $$k = \frac{1}{7}$$
--> $$m + n + p = 41*\frac{1}{7}$$ --> Sufficient

Option D
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Re: If seven times m is equivalent to both three times n and 2 times p, wh  [#permalink]

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04 Apr 2020, 09:17
Bunuel wrote:
If seven times m is equivalent to both three times n and 2 times p, what is the value of m + n + p?

(1) m – n = –4
(2) n + p = 5

Project DS Butler Data Sufficiency (DS3)

Analyzing the question:
7m = 3n = 2p. What is m + n + p?
Since we have all the ratios related m, n, and p, we can change all variables to the same one. For example, $$m + n + p = m + \frac{7m}{3 }+ \frac{7m}{2}$$. Then we can change the question to what is m? (Any variable works since we have the ratios).

Statement 1:
$$m - n = m - \frac{7m}{3} = -4$$. Can solve for m. Sufficient.

Statement 2:
$$n + p = \frac{7m}{3 }+ \frac{7m}{2} = 5$$. Can solve for m, sufficient.

Ans: D
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Re: If seven times m is equivalent to both three times n and 2 times p, wh   [#permalink] 04 Apr 2020, 09:17