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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Are there more girls than boys at a school?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:39) correct 38% (01:39) wrong based on 74 sessions

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[GMAT math practice question]

Are there more girls than boys at a school?

1) $$\frac{3}{7}$$ of the number of girls is more than $$\frac{1}{3}$$ of the number of boys
2) $$\frac{1}{3}$$ of the number of girls is more than $$\frac{2}{5}$$ of the number of boys

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Re: Are there more girls than boys at a school?  [#permalink]

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1
1) 3/7 girls >1/3 boys
girls> 7/9 boys
girls > 0.77 boys.
girls can be 0.8 boys or 1.2 boys.
Not sufficient.
2) 1/3 girls> 2/5 boys
girls >6/5 boys
girls>1.2 boys.
Hence no. of girls greater than boys. Sufficient.
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Re: Are there more girls than boys at a school?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

Are there more girls than boys at a school?

1) $$\frac{3}{7}$$ of the number of girls is more than $$\frac{1}{3}$$ of the number of boys
2) $$\frac{1}{3}$$ of the number of girls is more than $$\frac{2}{5}$$ of the number of boys

1) $$\frac{3}{7}$$ of the number of girls is more than $$\frac{1}{3}$$ of the number of boys

$$\frac{3}{7}$$ $$g$$ > $$\frac{1}{3}$$ $$b$$

Let g =7 & b = 6............3 > 2.........Answer is Yes

Let g = 14 & b =15............6 > 5.........Answer is NO

Insufficient

2) $$\frac{1}{3}$$ of the number of girls is more than $$\frac{2}{5}$$ of the number of boys

$$\frac{1}{3}$$ $$g$$ > $$\frac{2}{5}$$ $$b$$

Let g = 9 & b = 5............3 > 2.........Answer is Yes

Let g = 15 & b = 10........5 > 4.........Answer is Yes

Let g = 21 & b = 15............7 > 6.........Answer is Yes

There is a pattern here, number of girls must be greater than number of boys to hold true

Sufficient

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
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Re: Are there more girls than boys at a school?  [#permalink]

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (b for boys and g for girls) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2) together:
From condition 1:
$$(\frac{3}{7})g > (\frac{1}{3})b$$
$$=> 9g > 7b$$

From condition 2:
$$(\frac{1}{3})g > (\frac{2}{5})b$$
$$=> 5g > 6b$$
$$=> 6g > 5g > 6b$$
$$=> g > b$$

Both conditions together are sufficient.

Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1):

$$\frac{(3}{7})g > (\frac{1}{3})b$$
$$=> 9g > 7b$$

If $$g = 10$$ and $$b = 8$$, then the answer is ‘yes’.
If $$g = 8$$ and $$b = 8$$, then the answer is ‘no’.

Thus, condition 1) is not sufficient on its own.

Condition 2):

$$(\frac{1}{3})g > (\frac{2}{5})b$$
$$=> 5g > 6b$$
$$=> 6g > 5g > 6b$$
$$=> g > b$$

Thus, condition 2) is sufficient on its own.

Therefore, B is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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Re: Are there more girls than boys at a school?  [#permalink]

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1
DI Question : Are there more girls than boys at a school?
i.e. G>B?

Statement 1): $$\frac{3}{7}$$ of the number of girls is more than $$\frac{1}{3}$$ of the number of boys
3/7 G >1/3 B
G>1/7 B
So, No. of girls can be either greater or less than number of boys.
NOT SUFFICIENT

Statement 2): $$\frac{1}{3}$$ of the number of girls is more than $$\frac{2}{5}$$ of the number of boys
1/3 G > 2/5B
G>6/5 B
So, No. of girls is greater than number of boys.
SUFFICIENT

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