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# What is the number of girls in a class, if the total strength of the

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Math Expert
Joined: 02 Aug 2009
Posts: 5333

Kudos [?]: 6082 [0], given: 121

What is the number of girls in a class, if the total strength of the [#permalink]

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06 Nov 2017, 10:31
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Difficulty:

55% (hard)

Question Stats:

50% (01:11) correct 50% (01:00) wrong based on 48 sessions

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What is the number of girls in a class, if the total strength of the class is less than 35?

(1) There are at least 10 boys.
(2) The number of girls is equal to $$\frac{8}{13}$$ of total strength.

[Reveal] Spoiler: OA

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6082 [0], given: 121

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Joined: 25 Feb 2013
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Kudos [?]: 302 [0], given: 38

Location: India
GPA: 3.82
What is the number of girls in a class, if the total strength of the [#permalink]

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06 Nov 2017, 11:02
chetan2u wrote:
What is the number of girls in a class, if the total strength of the class is less than 35?

(1) There are at least 10 boys.
(2) The number of girls is equal to $$\frac{8}{13}$$ of total strength.

let the total strength be $$x$$ where $$x<35$$ is an integer

Statement 1: implies $$boys≥10$$, so number of $$girls=x-boys$$. There could be multiple values. Insufficient

Statement 2: implies $$girls = \frac{8x}{13}$$. but we don't know about $$x$$ so Insufficient

Combining 1 & 2 number of $$boys = x-\frac{8x}{13}=\frac{5x}{13}$$

it is given that $$\frac{5x}{13}≥10$$ and $$x<35$$. so the only value of $$x$$ that satisfies both these conditions is $$x=26$$

Hence number of $$girls = \frac{8*26}{13}=16$$

Option C

Last edited by niks18 on 06 Nov 2017, 11:08, edited 4 times in total.

Kudos [?]: 302 [0], given: 38

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Kudos [?]: 446 [0], given: 206

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Re: What is the number of girls in a class, if the total strength of the [#permalink]

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06 Nov 2017, 11:04
chetan2u wrote:
What is the number of girls in a class, if the total strength of the class is less than 35?

(1) There are at least 10 boys.
(2) The number of girls is equal to $$\frac{8}{13}$$ of total strength.

Hi Chetan!

What is the meaning of strength? It kind of got me confused...
I believe it is the total number.

1. Let's say that we have 34 people. we can have 10 boys and 24 girls, or we can have 11 boys and 24 girls. Moreover, not having an exact number for the entire class opens the doors to even more possibilities. First statement is insufficient, and we can remove A and D from the answer choices.

2. Since we deal with integers, there are 2 options for the class size. either 13 or 26. thus, girls can be either 8 or 16. Since we have 2 different outcomes, B is out.

1+2.
we can have either 13 or 26 people in the class.
we must have at least 10 boys and either 8 or 16 girls.
using this information, we know that the class size is 26, we have 10 boys and 16 girls.

Kudos [?]: 446 [0], given: 206

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Kudos [?]: 28 [0], given: 106

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What is the number of girls in a class, if the total strength of the [#permalink]

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08 Nov 2017, 13:45
Condition 1 clearly is insufficient, so we rule out A and D
Condition 2 - 8/13 are girls. Again, it does not give us any info about boys.

Combining: 1+2 = 5/13.x >=10 where x is the total number

x>=26,
now since number of girls is 8/13 and only 26 is divisible by 13, the total number of students is 26. This satisfies the question stem.
No of girls = 16 and boys = 10

Option C

Kudos [?]: 28 [0], given: 106

What is the number of girls in a class, if the total strength of the   [#permalink] 08 Nov 2017, 13:45
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