Data Sufficiency
Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.
 12 men and 8 women can complete a piece of work in 10 days. How many days will it take for 15 men and 4 women to complete the same work?
A. 15 men can complete the work in 12 days.
B. 15 women can complete the work in 16 days.
C. The amount of work done by a woman is three  fourth of the work done by a man in one day.

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As per the given all details in above question , we can say
Given , 12 men and 8 women can complete a piece of work = 10 days
Let 15 men and 4 women to complete the same work in D days .
From statement A , 15 men can complete the work = 12 days.
From statement B , 15 women can complete the work = 16 days.
From statement C , Women = ( 3 / 4 ) x men ⇒ 4W = 3M
According to question ,
( 12M + 8W ) x 10 = ( 15M + 4W ) x D
⇒ ( 4 x 4W + 8W ) x 10 = ( 5 x 4W + 4W ) x D ⇒ 24W x 10 = 24W x D ⇒ D = 10 daysCorrect Option: D
As per the given all details in above question , we can say
Given , 12 men and 8 women can complete a piece of work = 10 days
Let 15 men and 4 women to complete the same work in D days .
From statement A , 15 men can complete the work = 12 days.
From statement B , 15 women can complete the work = 16 days.
From statement C , Women = ( 3 / 4 ) x men ⇒ 4W = 3M
According to question ,
( 12M + 8W ) x 10 = ( 15M + 4W ) x D
⇒ ( 4 x 4W + 8W ) x 10 = ( 5 x 4W + 4W ) x D ⇒ 24W x 10 = 24W x D ⇒ D = 10 days
Any two of the three statements are sufficient to answer the question. Hence, anyone of the statements can be dispensed with.
 The difference between the compound interest and the simple interest at the same rate on a certain amount at the end of two years is $ 12.50. What is the rate of interest?
A. Simple interest for two years is $ 500.
B. Compound interest for two years is $ 512.50.
C. Amount on simple interest after two years becomes $ 5500.

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As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
From (A) alone :Rate = (CI  SI) x 2 x 100 = 25 x 100 = 5% SI 500
Correct Option: E
As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
From (A) alone:Rate = (CI  SI) x 2 x 100 = 25 x 100 = 5% SI
From (B) alone :
CI = $512.5
∴ SI = $512.5 − $12.5 = $ 500
Again,Rate = (CI  SI) x 2 x 100 SI Rate = 25 x 100 = 5% 500
From (C) alone :
Suppose Principal = P and Rate of Interest = r%Then, P 1 + r ^{2} = 5500 + 12.5 = 5512.5 ...(1) 100 and, P + 2rP = 5500 100 or, P 1 + 2r = 5500 ...(2) 100
Dividing (1) by (2) we have
[1 + ( r / 100 )]^{2} /[1 + ( 2r / 100 )] = 5512.5 / 5500 ....(3)
This is a quadratic equation which has only one variable, r. It can be solved. Hence, value of r can be obtained.
Note : is satisfied with the value r = 5.
So, it confirms that equation is solvable.
 What will be the sum of the ages of father and the son after five years?
A. Father’s present age is twice son’s present age.
B. After ten years the ratio of father’s age to the son’s age will become 12 : 7.
C. Five years ago the difference between the father’s age and son’s age was equal to the son’s present age.

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On the basis of above given details in question ,
Let father’s present age is F and son’s present age is S .
From statement A , Father’s present age = 2 x son’s present age
⇒ F = 2S
From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
From statement C , 5 years ago , father’s age  son’s age = son’s present age
⇒ ( F  5 )  ( S  5 ) = S
From statement B and A , we have
⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
⇒ 14S + 70 = 12S + 120 ⇒ 14S  12S = 120  70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
Sum of the ages of father and the son after five years = 55 + 30 = 85 yearsCorrect Option: E
On the basis of above given details in question ,
Let father’s present age is F and son’s present age is S .
From statement A , Father’s present age = 2 x son’s present age
⇒ F = 2S
From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
From statement C , 5 years ago , father’s age  son’s age = son’s present age
⇒ ( F  5 )  ( S  5 ) = S
From statement B and A , we have
⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
⇒ 14S + 70 = 12S + 120 ⇒ 14S  12S = 120  70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
Sum of the ages of father and the son after five years = 55 + 30 = 85 years
Any two of the three statements are sufficient to answer the question (As to find the two unknowns we need two equations). Hence, anyone of the statements can be dispensed with.
 What will be the cost of fencing a circular plot?
∏ = 22 .... 7
A. Area of the plot is 616 m^{2}.
B. Cost of fencing a rectangular plot whose perimeter is 120 m is $780.
C. Area of a square plot with side equal to the radius of the circular plot is 196 m^{2}.

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As per the given question , we can say From statement A , Area of the plot = πr^{2} = 616 m^{2} .
⇒ ( 22 / 7 ) x r^{2} = 616 ⇒ r^{2} = 616 x ( 7 / 22 ) = 28 x 7 = 196
⇒ r = 14 cm
From statement B , Cost of fencing a rectangular plot = $ 780 and perimeter =120 m
From statement C , Area of a square plot = a^{2} = 196 m^{2}
⇒ a = √196 = 14
∴ a = 14 = radius of the circular plot
From statement A , we have
Area of the plot = 616 m^{2}
∴ Cost of fencing a circular plot = Area x Cost of fencing a rectangular plot = 616 x 780 = $ 480480Correct Option: C
As per the given question , we can say
From statement A , Area of the plot = πr^{2} = 616 m^{2} .
⇒ ( 22 / 7 ) x r^{2} = 616 ⇒ r^{2} = 616 x ( 7 / 22 ) = 28 x 7 = 196
⇒ r = 14 cm
From statement B , Cost of fencing a rectangular plot = $ 780 and perimeter =120 m
From statement C , Area of a square plot = a^{2} = 196 m^{2}
⇒ a = √196 = 14
∴ a = 14 = radius of the circular plot
From statement A , we have
Area of the plot = 616 m^{2}
∴ Cost of fencing a circular plot = Area x Cost of fencing a rectangular plot = 616 x 780 = $ 480480
(B) is necessary because only this statement gives the rate of fencing. Anyone of (A) or (C) gives the value of radius, which enables us to find the circumference.
Hence, either (A) or (C) can be dispensed with.