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# If there are 56 people attending a birthday party which of the followi

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Math Expert
Joined: 02 Sep 2009
Posts: 43853
If there are 56 people attending a birthday party which of the followi [#permalink]

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10 May 2017, 01:26
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5% (low)

Question Stats:

96% (00:37) correct 4% (01:06) wrong based on 63 sessions

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If there are 56 people attending a birthday party which of the following is a possible ratio of women to men at the party?

A. 10 : 9
B. 11 : 4
C. 30 : 1
D. 1 : 7
E. 2 : 23
[Reveal] Spoiler: OA

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Re: If there are 56 people attending a birthday party which of the followi [#permalink]

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10 May 2017, 02:36
Bunuel wrote:
If there are 56 people attending a birthday party which of the following is a possible ratio of women to men at the party?

A. 10 : 9
B. 11 : 4
C. 30 : 1
D. 1 : 7
E. 2 : 23

The number of women and the number of men must be integer.

A. $$\text{the ratio of women to men} = \frac{\text{women}}{\text{men}}=10 : 9\implies \frac{\text{women}}{\text{all}}=\frac{10}{19}\implies \text{women}=56 \times \frac{10}{19}$$

56 isn't divisible by 19, so eliminate this choice.

B. $$\frac{\text{woman}}{\text{all}}=\frac{11}{15}$$.

56 isn't divisible by 15, so eliminate this choice.

C. $$\frac{\text{woman}}{\text{all}}=\frac{30}{31}$$.

56 isn't divisible by 31, so eliminate this choice.

D. $$\frac{\text{woman}}{\text{all}}=\frac{1}{8} \implies \text{woman}=56 \times \frac{1}{8}=7 \implies \text{men}=49$$.

This choice is the correct answer.

E. $$\frac{\text{woman}}{\text{all}}=\frac{2}{25}$$.

56 isn't divisible by 25, so eliminate this choice.
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Re: If there are 56 people attending a birthday party which of the followi [#permalink]

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10 May 2017, 08:53
the sum of the ratio shud be a factor of the total...
ans D
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If there are 56 people attending a birthday party which of the followi [#permalink]

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10 May 2017, 09:22
My approach:
Prime factorization of 56 = 2^3 x 7
If you look at the answer choices you would realize only answer D would leave an integer.

D - 1/8 x 56 = 7 women; 7/8 x 56 = 49 men.
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Re: If there are 56 people attending a birthday party which of the followi [#permalink]

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12 May 2017, 12:38
Bunuel wrote:
If there are 56 people attending a birthday party which of the following is a possible ratio of women to men at the party?

A. 10 : 9
B. 11 : 4
C. 30 : 1
D. 1 : 7
E. 2 : 23

Since there are 56 TOTAL people at the party, we can create the following expression:

56/(ratio of men + ratio of women) = integer
Thus, when we sum the ratio of men and the ratio of women, we must get a factor of 56. Let’s test the answer choices:

A) 10 : 9

Since 10 + 9 = 19, and 19 is not a factor of 56, answer choice A is not correct.

B) 11 : 4

Since 11 + 4 = 15, and 15 is not a factor of 56, answer choice B is not correct.

C) 30 : 1

Since 30 + 1 = 31, and 31 is not a factor of 56, answer choice C is not correct.

D) 1 : 7

Since 1 + 7 = 8, and 8 is a factor of 56, answer choice D correct.

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Re: If there are 56 people attending a birthday party which of the followi [#permalink]

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13 May 2017, 17:35
Test solutions using the unknown multiplier:

A. 19x = 56 (does not equal a number)
B. 15x = 56 (does not equal a number)
C. 31x = 56 (does not equal a number)
D. 8x = 56 (EQUALS A NUMBER)
E. 25x = 59 (does not equal a number)

Re: If there are 56 people attending a birthday party which of the followi   [#permalink] 13 May 2017, 17:35
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# If there are 56 people attending a birthday party which of the followi

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