1. HCF of two numbers, each consisting of four digits, is 103 and their LCM is 19261. The difference of the numbers is

A. [latex]\frac{6}{8}[/latex] B. [latex]\frac{5}{9}[/latex] C. [latex]\frac{5}{8}[/latex] D. [latex]\frac{4}{8}[/latex]

Answer: Option A
Explanation :
Product of two Numbers = LCM × HCF
x × y = 103 × 19261
= 103 × 103 × 11 × 17 = 1133 × 1751
Difference = [latex]\frac{6}{8}[/latex]
2. [latex]2^{2^{4}}[/latex]divided by [latex]2^{2^{3}}[/latex] is equal to:.

A. [latex]2^{2}[/latex] B. [latex]2^{1}[/latex] C. [latex]2^{-2}[/latex] D. [latex]2^{-1}[/latex]

Answer: Option A
Explanation
[latex]2^{2^{4}}[/latex]divided by [latex]2^{2^{3}}[/latex]
=[latex]2^{8}[/latex]divided by [latex]2^{6}[/latex]
= [latex]2^{2}[/latex]
3. Arrange the following fractions in ascending order. [latex]\frac{7}{10}[/latex], [latex]\frac{3}{8}[/latex], [latex]\frac{4}{5}[/latex]

A. [latex]\frac{3}{8}[/latex], [latex]\frac{7}{10}[/latex], [latex]\frac{7}{10}[/latex] C. [latex]\frac{4}{5}[/latex], [latex]\frac{3}{8}[/latex], [latex]\frac{7}{10}[/latex] D. [latex]\frac{7}{10}[/latex], [latex]\frac{3}{8}[/latex], [latex]\frac{4}{5}[/latex]

Answer: Option A
Explanation
[latex]\frac{7}{10}[/latex] = 0.7
[latex]\frac{3}{8}[/latex] = 0.375
i.e, [latex]\frac{3}{8}[/latex] < [latex]\frac{7}{10}[/latex] < [latex]\frac{4}{5}[/latex]
[latex]\frac{4}{5}[/latex] = 0.8
4. By what least number should 192,000 be divided so as to become a perfect cube?

A. 2 B. 5 C. 3 D. 7

Answer: Option C
Explanation
[latex]\frac{192000}{2}[/latex] = 96,000 Not a perfect cube.
[latex]\frac{192000}{3}[/latex] = 64,000 A perfect cube
5. Find the value of: 3 + 0.03 + 0.003 + 0.0003

A. 12 B. 3.0333 C. 3.3333 D. 6.0333

Answer: Option B
Explanation
3 + 0.03 + 0.003 + 0.0003
= 3.0333

1. 2 men and 7 women complete a work in 14 days, while 3 men and 8 women complete the same work in 11 days. I n how many days will 8 men and 6 women complete 3 times of this work ?

A. 14 B. 21 C. 24 D. 28

Answer: Option B
Explanation
Let work done by a man in a day = x units
Let work done by a woman in a day = y units
(2x + 7y) × 14 = (3x + 8y) 11
28x + 98 y = 33x + 88y
5x = 10 y
x = 2y.
work (2x + 7y) × 14
= (2 × 2y + 7y) × 14 = 154 y.
3 times work will be done in
[latex]\frac{(154y) * 3}{8x + 6y}[/latex]
[latex]\frac{(154y) * 3}{22y}[/latex] = 21 days
2. To do a certain piece of work B takes four times as long as A and C together and C takes three times as long as A and B together. If all the three working together complete the work in 12 days, how long (in days) would A alone take to complete the work?

A. [latex]21 \frac{9}{11}[/latex] B. [latex]26 \frac{2}{3}[/latex] C. 48 D. 60

Answer: Option A
Explanation
Let A alone takes x days to do the work.
Let B alone takes y days to do the work.
Let C alone takes 2 days to do the work.
According to the question
[latex]\frac{1}{x}[/latex] ÷ [latex]\frac{1}{2}[/latex] = [latex]\frac{4}{y}[/latex]
[latex]\frac{1}{x}[/latex] ÷ [latex]\frac{1}{2}[/latex] = [latex]\frac{3}{7}[/latex]
Also [latex]\frac{1}{x}[/latex] ÷ [latex]\frac{1}{y}[/latex] ÷ [latex]\frac{1}{2}[/latex] = [latex]\frac{1}{12}[/latex]
Solving for x
x = [latex]\frac{4 * 60}{11}[/latex] = [latex]21 \frac{9}{11}[/latex]
3. If 6 men and 8 women can do a piece of work in 10 days while 5 men and 15 women can do the same work in 8 days? I n how many days will 15 men and 20 women do the same work?

A. 2 B. 3 C. 4 D. 5

Answer: Option C
Explanation
Let work done by a man = x units in one day
Let work done by a woman = y units in one day
According to the question
(6x + 8y) 10 = (5x + 15y)8
60x + 80y = 40x + 120y
20x = 40y = x = 2y
i.e, Time = [latex]\frac{(6x ÷ 8y) * 10}{15x ÷ 20y}[/latex]
= [latex]\frac{200y}{50y}[/latex] = 4 days
4. 8 men and 12 women can do a piece of work in 5 days, while 6 men and 8 women can do it in 7 days. The time (in days) taken by two women and one man to do the same work is

A. 21 B. 28 C. 35 D. 40

Answer: Option C
Explanation
Let x units of work be done by a man in one day.
Let y units of work be done by a woman in one day
(8x + 12y)5 = (6x + 8y)7
40x + 60y = 42x + 56y
2x = 4y
x = 2y
i.e, Time = [latex]\frac{(8x ÷ 12y) * 5}{x ÷ 2y}[/latex]
= [latex]\frac{(8x * 5 * y)}{2y}[/latex] = 35 days
5. Two pipes X and Y can fill a tank in 15 and 20 minutes respectively. If both the pipes are opened together after how much time pipe y should be turned off so that the tank is full in 12 minutes?

A. 3 minutes B. 4 minutes C. 5 minutes D. 6 minutes

Answer: Option B
Explanation
Let Tank capacity be 300 litres.
i.e, filling speed of x
[latex]\frac{300}{20}[/latex] = 20 l/min
filling speed of y
[latex]\frac{300}{15}[/latex] = 15 l/min
Let pipe of be turned off after + minutes
According to the question
20 × 12 + 15 × t = 300
t = 4 mins

1. In how many ways can 5 boys and 4 girls can be seated in a row so that they are in alternate position.

A. 2780 B. 2880 C. 2800 D. 2980

Answer: Option B
Explanation
First boys are seated in 5 position in 5! Ways, now remaining 4 places can be filled by 4 girls in 4! Ways, so number of ways = 5! 4! = 2880
2. In how many ways 5 African and five Indian can be seated along a circular table, so that they occupy alternate position.

A. 5! 5! B. 4! 5! C. 5! 4! D. 4! 4!

Answer: Option B
Explanation
First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!
3. There is meeting of 20 delegates is to be held in a hotel. In how many ways these delegates can be seated along a round table, if three particular delegates always seat together.

A. 17! 3! B. 18! 3! C. 17! 4! D. can’t be determined

Answer: Option A
Explanation
Total 20 persons, 3 always seat together, 17 + 1 = 18 delegates can be seated in (18 -1)! Ways = 17! And now that three can be arranged in 3! Ways. So, 17! 3!
4. In how many 8 prizes can be given to 3 boys, if all boys are equally eligible of getting the prize.

A. 512 B. 343 C. 256 D. 526

Answer: Option A
Explanation
Prizes cab be given in 8*8*8 ways = 512 ways
5. In party there is a total of 120 handshakes. If all the persons shakes hand with every other person. Then find the number of person present in the party.

A. 15 B. 16 C. 17 D. 18

Answer: Option B
Explanation
[latex]{N}_{{C}_{2}}[/latex] = 120 (N is the number of persons)