Data Sufficiency Actual Question in CMAT 2023 Slot – 2

Q1. Given below are two statements :
Statement I: The ratio of the son’s age to the father’s age is 1 : 5. The product of their ages is 245. The ratio of the son’s age to the father’s age after 9 years will be 3 : 5.
Statement II: A milkman adds 30 litres of water to 70 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be 28 : 72.
In the light of the above statements, choose the correct answer from the options given below.
A Both Statement I and Statement II are true
B Both Statement I and Statement II are false
C Statement I is true but Statement II is false
D Statement I is false but Statement II is true

EXPLANATION

B
Statement I:
It is given that the ratio of son’s age to father’s age is 1:5
Let the son’s age be x and father’s age be 5x.
(x)(5x) = 245
x = 7
Therefore, son’s age is 7 years and father’s age is 35 years.

After 9 years, son’s age is 16 years and father’s age is 44 years.
Ratio = 16 : 44 = 4 : 11
Statement II:
Initially – 70L milk and 30L water
After selling 1/5th of the solution – 56L milk and 24L water
Adding water – 56L milk and 44L water
water:milk = 44:56 = 11:14
The answer is option B.

Q2. Given below are two statements :
Statement I: If ‘some students are intelligent’ is true, then ‘some students are not intelligent’ is also true.
Statement II: If ‘all logicians are mathematician’ is true, then ‘some non-mathematicians are not logicians’
will be true.
In the light of the above statements, choose the correct answer from the options given below.
A Both Statement I and Statement II are true
B Both Statement I and Statement II are false
C Statement I is true but Statement II is false
D Statement I is false but Statement II is true

EXPLANATION

D

Statement I is false because some students are intelligent implies two cases:

all the students are intelligent.some students are not intelligent.
Any of these can be correct. Hence, statement 1 is also false.
Statement II is true since all the logicians are mathematicians, which implies that all the non-mathematicians
can’t be logicians, which implies some non-mathematicians are not logicians.
The correct option is D.