Question: The population of a village is calculated by adding the number of males and the number of females. If this year male population increased by 10% as compared to last year, what is the net percentage change in total population of the village?

1. The number of females as compared with last year increased this year by 5%
2. The ratio of the number of females and the males was 2 : 3 last year

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Solution with Explanation:
Approach Solution (1):

Last year: males = 100x, females = 100y
Thus year: males = 110x, females =?
Net percentage change = \(\frac{(T(P) - L(P))*100}{L(P)}\)

Where T(P): Total population this year and L(P): Total population last year
S1: This year : males = 110x females = 105y
Net percentage change = \(\frac{(100x+105y-(100x+100y))*100}{100(x+y)}=\frac{10x+5y}{(x+y)}\)

We do not know value of x and y
Not sufficient

S2: Ratio of: \(\frac{100y}{100x}=\frac{2}{3}\)
Not sufficient
Combining both statements:
y = \(\frac{2x}{3}\)
Net percentage change = \(5(\frac{2x+\frac{2x}{3}}{x+\frac{2x}{3}})\)
x will get cancelled out leaving us with a unique value
Sufficient

Correct Option: C

Approach Solution (2):

S1: The number of females as compared with last year increased this year by 5%

Based on this information, we cannot deduce the net percentage change in total population of the village. We need additional information on the number or the ratio of the number of females this year as compared with number of females last year.
Not sufficient

S2: The ratio of the number of females and the males was 2 : 3 last year

Based on this information, we cannot deduce the net percentage change in the total population of the village. We need additional information on the increase / decrease of the number of females this year as compared with number of females last year.
Not sufficient
(1) + (2)
Having both the information, we can deduce the net percentage change in total population of the village: 2/5 * 5% + 3/5 * 10% = 8% increase

Correct Option: C

Approach Solution (3):

Last year
Male = x, Female =?, Total population (TP) =?
This year
Male = 1.1x, Female =?, TP =?
Asked: %age change in TP = (TP (this year) – TP (last year) / TP (this year)
S1: says, last year female = y, but this year = 1.05y
So %age change in TP = \(\frac{([1.1x+1.05x] - [x+y])}{(x+y)}\)
Not sufficient

S2: Females/ Males = 2x/ 3x
Not sufficient
(1) + (2)
Last year
Male = 3x, Female = 2x
TP = 5x
This year

Male = 10% inc. of 3x = (3.3x)
Female = 5% inc. of 2x = (2.1x)
TP = 5.4x

Net % change in TP = \(\frac{(5.4x - 5x)}{5x}\)
Net % change in TP = \(\frac{0.4x}{5x} = 8 \)%

Correct Option: C

“The population of a village is calculated by adding the number of males and the number of females. If this year male population increased by 10% as compared to last year, what is the net percentage change in total population of the village?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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