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
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
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
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. 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
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
5. Find the arithmetic mean of 8 no.between 1 and 10.
(a) 2.5
(b) 5.5
(c) 3.5
(d) 4.5
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
6. 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
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
7. 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
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.
8.The length of a train and that of a platform are equal. If a speed of train 90 km/hr then train crosses the platform in one minute, then the length of the train (in metres) is :
(a) 500
(b) 600
(c) 750
(d) 900
Sol. Le the length of train be x metre
Speed = 90 km/hr
= (90 * 5) /18 meter/sec.
= 25 metre/sec.
so Distance covered in 60 sec.
= 25 * 60 = 1500 metres
Now, according to question.
2x = 1500
so x = 750 meter
9.A number when divided by the sum of 555 and 445, gives two times their difference as quotient and 30 as the remainder. The number is.
(a) 220030
(b) 22030
(c) 1220
(d) 1250
Sol. According to question,
Divisor = 555 + 445 = 1000
Dividend = ?
Quotient = (555 – 445) * 2
= 110 * 2 = 220
Remainder = 30
Dividend = (Divisor * Quotient) + Remainder
= (1000 * 220) + 30
= 220000 + 30 = 220030
10.A number of friends decided to go on a picnic and planned to spend Rs. 108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute Rs. 3 extra. The number of them who attended the picnic was:
(a) 15
(b) 12
(c) 9
(d) 6
Sol. Let the number of friends be x.
so 108/(x – 3) – 108/x = 3
108 * 3 /x(x -3) = 3
=> x^2 – 3x = 108
=> x^2 – 12x + 9x – 108 = 0
=> x(x-12) + 9 (x -12) = 0
(x – 12) (x + 9) = 0
X = 12
Number of friends who attended
= 12 – 3 = 9
