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DATA SUFFICIENCY Questions  – Problems on Ages a)If the data in statement I alone are sufficient to answ...

# Data Sufficiency Questions - Problems on Ages

DATA SUFFICIENCY Questions  – Problems on Ages

a)If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

b)If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

c)If the data in both the statement I and II together are necessary to answer the question.

d)If the data in either statement I alone or statement II alone are sufficient to answer the question.

e)If the data in both the statement I and II are not sufficient to answer the question.

1.What is the present age of Parimala?

1. Parimala is 5 times younger than Rajini

2. The sum of the ages of Supriya and Rajani is 80 years Supriya’s age  is thrice the age of Rajani

Explanation:

Statement 1 alone:

Parimala is 5 times younger than Rajani

Parimala = 1/5 x Rajani

Statement 1 alone  is not sufficient to answer the question

Statement 2 alone :

Supriya +  Rajani = 80 years

Supriya = 3 x Rajani

= > Supriya: Rajani – 3: 1

Age of Rajani = 80 x ¼ = 20

Statement 2 alone is not sufficient to answer the question

Both statements together:

Age of Rajani is 20 years

Parimala = 1/5 x Rajini

= > Parimala = 20 x 1/5 = 4 years

Hence, both the statements I and II together are necessary to answer the question.

2.What is the present age of the mother?

1. The present age of mother and son are in the ratio of 4:1, respectively.

2. 20 years hence the ratio of the ages of mother and son will be 16:9, respectively.

Explanation :

Statement 1 alone :

The ratio of the  ages of mother and son is 4:1

From this, we can't find the age of the mother

So statement 1 alone is not sufficient to answer the question

Statement 2 alone :

After 20 years, the ages of mother and son will be in the ratio of 16: 9 respectively

The statement alone is not sufficient to answer the question

Both statements 1 and 3 together :

Let the present ages of mother and son are 4x and x respectively

After 20 years => Mother /Son = 4x + 20/x +20 = 16/9

= >36x +180 = 16x +320

= > 20x =140

= > x=7

The age of the mother is 4x 7 = 28 years

So both statements together are needed to answer the question

3.What is the age of Divya after  8 years?

1.Divya is 3 times elder than Bhavya

2.Surya’s age is thrice the age of Bhavya

Explanation :

Statement 1 alone :

Divya = 3 x Bhavya

Statement 2 alone:

Surya = 3 x Bhavya

Both statement together :

Divya = Surya = 3 Bhavya

The age of Divya cannot be found

Both the statement together are not sufficient to answer the question.

4.What was the age of Srimanth 6 years ago?

1.The ratio between the ages of Srimanth and Sameer is 7:5 respectively

2.Srimanth is 8 years elder than Sameer

Explanation:

Statement 1 alone :

Srimanth : Sameer = 7:5

Statement  2 alone:

Srimanth – Sameer = 8 years

Both statement 1 and 2 together :

Let the ages of Srimanth and Sameer be 7x and 5x respectively

Srimanth – Sameer => 7x -5x = 8 years => x = 4 years

So the present age of Sameer is (7 x 4) = 28 years

6 years ago, the age of Srimanth was => 28-6 = 22 years

Hence, data in both the statements I and II together are necessary to answer the question.

5.What is the present of Prasad?

1.Prasad is 8 years younger than Sahithi

2.The ratio between the ages of Prasad  and Madhuri is 5:8 respectively

Explanation :

Statement 1 alone :

Statement 2 alone:

Both statements together :

Prasad = Sahithi + 8 years

We cannot find the age of Prasad  using both statements together

6.What was the age of the mother, when her youngest daughter was born?

1.The present age of the mother is 36 years

2.The mother's age is 3/2 times the sum of the ages of her two daughters born at intervals of 4 years

Explanation :

Statement 1 alone :

Mother’s present age = 36

Statement 1 alone is not sufficient

Statement 2 alone :

Let the age of the youngest daughter be x. Then the age of another daughter will be (x + 4)

Mother’s age = 3/2 ( (x+ (x+4))

Statement 2 alone is not sufficient

Both statements together :

Mother’s present age = 3/2 ( x +(x+4)

= > 36 = 3/2 (2x+4)

= > 2x+ 4 = 24

=>x = 10 years

The age of the mother when the younger daughter was born =>36-10 = 26 years

Both statements together are sufficient to answer the question

7.What is the present age of Murty?

1.After 48 years, the age of Murty will be 3 times his present age

2.14 years ago, Murty celebrated his 10th birthday

Explanation :

Statement 1 alone :

Let the present age of Murty be x.

x + 48 = 3x => 2x = 48 => x = 24

So statement 1 alone is sufficient to answer the question

Statement 2 alone :

14 years ago, Murty celebrated his 10th birthday

So 14 years  year , his age was 10 years => Murty’s present age = 14 + 10 = 24 years

Statement 2 alone is sufficient to answer the question

Therefore, either statement 1 alone or statement 2 alone is sufficient to answer the question

8.How old each of Ramesh and Suresh?

1.6         years ago, Ramesh was 3 times elder than Suresh

2.After  8 years, Ramesh will be twice as old as Suresh will be

Explanation:

Statement 1 alone :

6 years ago, the ratio of Ramesh and Suresh = 3:1

Statement 1 alone is not sufficient to get the answer

Statement 2 alone :

8 years hence, the ratio of Ramesh and Suresh will be 2:1

Statement 2 alone is not sufficient to get the answer

Statements 1 and 2 together :

Let the age of Ramesh and Suresh 6 years ago be 3x and x respectively

After 8 years => Ramesh/Suresh =( 3x + 6+ 8)/(x +6 +8) = 2/1

= >(3x + 14)/ (x + 14) = 2/1

= >(3x + 14) = (2x + 28)

= >x= 14

Present age of Ramesh and Suresh are => (3x + 6) and (x+6) respectively

=> 48 and 20 years respectively

So data given in both statements together are sufficient

9.Two siblings have some peculiarities about their ages. What are their present ages?

1.Their present ages are odd integers

2.The sum of their ages is 15 years

Explanation :

Statement 1 alone :

The present ages of two siblings are odd integers

Many possibilities are there

Statement 1 alone is not sufficient to answer the question

Statement 2 alone:

The sum of their ages is 15 years

The possibilities are (14,1),(13,2),(12,3),(11,4),(10,5), (9,6) and (8,7)

We have more than one possible answer

So statement 2 alone is not sufficient to answer the question

Combining both statements :

The Sum of their present ages is 15 years and their ages are odd integers

We can get only one combination i.e (13,2)

Then their ages are 13 years and 2 years.

Both statements together are sufficient to answer the question.

10.Three brothers A, B, and C are of different ages. What is the age of  C 5 years ago?

1.A is 4 years elder than B

2.The sum of the ages of B and C is 19  years and the product of their ages is 88 years

Explanation:

Statement 1 alone :

The difference between the ages of A and B is given.

But we don’t have any information about C

So statement 1 alone is not sufficient to answer the question

Statement 2 alone:

The sum of the ages of B and C is 19  => B+C = 19

Product of the ages of B and C is => BC = 88

(B-C)2  = (B+C)2 -4BC

= >(B-C)2 = 192  - (4 x 88)

= >(B-C)2= 361-352

= >(B-C)2= 9

=>(B-C)= 3

On solving , B = 11 and C= 8

Therefore, the age of C 5 years ago was (8-5) = 5 years

Statement 2 alone is sufficient to answer the question