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
Answer : C
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.
Answer: C
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
Answer: E
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
Answer: C
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
Answer : E
Explanation :
Statement 1 alone :
Prasad =Sahithi + 8 years
Statement 2 alone:
Prasad: Madhuri = 5 : 8
Both statements together :
Prasad = Sahithi + 8 years
Prasad : Madhuri = 5 :8
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
Answer: A
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
Answer
: D
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
Answer : C
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
Answer: C
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
Answer
: B
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