1. x is a five-digit number. The digit in ten thousand’s place is 1. The number formed by its digit in unit’s and ten’s places is divisible by 4. The sum of all the digits is divisible by 3. If 5 and 7 also divide x, then x will be
(a) 14040
(b) 12060
(c) 10020
(d) 10080
Sol:
No number except 10080 is divisible by 7.
further,80 is divisible by 4.
1+0+0+8+0 = 9 is divisible by 3 and 10080 is also divisible by 5.
2. What is the weight of a cubical block of ice 50 cm in length, if one cubic metre of ice weights 900 kilograms?
(a) 113 kg
(b) 113.5 kg
(c) 112.5 kg
(d) 114 kg
Sol:
volume of the cubical block of ice = 50*50*50 cm^3
= (50*50*50)/(100*100*100) m^3 = 1/8 m^3
weight of the cube = 1/8*900 = 112.50 kg
3. If A, B and C are three numbers, such that, the LCM of A and B is B and the LCM of B and C is C, then the LCM of A, B and C is
(a) A
(b) B
(c) C
(D) (A+B+C)/3
Sol:
LCM of A & B is B => B is a multiple of both A & B
Again,
LCM of B & C is C => C is a multiple of both B & C
so LCM of ABC = C
4. In a class of 64 students, 50% of the students have taken Sociology and 75% of the students have taken Political Science. All Students have chosen either one subject. How many students have taken both the subjects?
(a) 12
(b) 18
(c) 14
(d) 16
5. Six men earn as much as seven women, two women earn as much as three boys, four boys earn as much as five girls. If a girl earns Rs.16 a week, what does a man earn per week?
(a) Rs.35
(b) Rs.20
(c) Rs.40
(d) Rs.30
Sol:
6 men = 7 women;
2 women = 3 boys;
4 boys = 5 girls;
Now earning of a girls per week = Rs. 16
so Earning of 1 boy = 5/4*16 = 20
Earning of 1 women = 3/2*20 = 30
Earning of 1 man = 7/6*30 = 35
6. Find the arithmetic mean of 8 no.between 1 and 10.
(a) 2.5
(b) 5.5
(c) 3.5
(d) 4.5
Sol:
8 arithmetic mean between 1 and 10
= 2,3,4,5,6,7,8,9
Their mean = (2+3+4+5+6+7+8+9)/8 = 5.5
7. In an examination, A obtain 10% less than the minimum number of marks required for passing, B obtains 11(1/9) less than A, and C obtains 41(3/17)% less than the number of marks obtained by A and B together. Does C pass or fail?
(a) Pass
(b) Fail
(c) Can’t say
(d) Data inadequate
8. The marked price of a shirt and a trouser are in the ratio 2 : 3. The shopkeeper gives 30% discount on the shirt. If the total discount is 20%. Then, the discount offered on the trouser is –
(a) 12(1/2)%
(b) 33(1/3)%
(c) 13(1/3)%
(d) 8(1/3)%
9. A, B and C are partners in a business. A, whose money has been used for 4 months, claims 1/8 of the profit. B, whose money has been used for 6 months, claims 1/3 of the profit. C had invested Rs. 1560 for 8 months. How much money did A and B contribute together?
(a) 720
(b) 1560
(c) 2000
(d) 1280
Sol:
Ratio of their profit= 1/8 : 1/3:(1-(1/8+1/3))
= 1/8 : 1/3 : 13/24
= 3:8:13
Now,for A & C
A*4 :c*8 = 3:13
A*4 :1560*8 = 3:13
A = (1560*8*3)/(4*13) = 720
For B & C,
B*6 :c*8 = 8:13
B*6 :1560*8 = 8:13
B = (1560*8*8)/(6*13) = 1280
Contribution by A & B together
= 720+1280= 2000
10. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. Then my age and my son’s age are respectively:-
(a) 42 yrs, 14 yrs
(b) 45 yrs, 15 yrs
(c)36 yrs, 12 yrs
(d) 48 yrs, 16 yrs
Sol:
Let the present age of my son = x yrs.
Then,the present age of mine = 3x yrs.
(3x+5)=2(1/2)(x+5)
x = 15 yrs.
Father’s age = 45 yrs.
Son’s age = 15 yrs.
