NUMBERS
1.Which is not the prime number?
43 | |
57 | |
73 | |
101 |
Question 1 Explanation:
A positive natural number is called prime number if nothing divides it except the number itself and 1. 57 is not a prime number as it is divisible by 3 and 19.
- How many terms are there in 3,9,27,81……..531441?
25 | |
12 | |
13 | |
14 |
Question 2 Explanation:
3, 9, 27, 81…………..531441 form a G.P.
with a = 3 and r = 9/3 = 3
Let the number of terms be n
According to the formula, N^{th} term of the G.P is represented as T_{n} = a x r^{n-1}
Then 3 x 3^{n-1} = 531441
∴ 3^{n} = 3^{12}
∴ n = 12
- If the average of four consecutive odd numbers is 16, find the smallest of these numbers?
A | 5 |
7 | |
13 | |
D | 11 |
Question 3 Explanation:
Let the numbers be x, x+2, x+4 and x+6
Then (x + x + 2 + x + 4 + x + 6)/4 = 16
∴ 4x + 12 = 64
∴ x = 13
- If the sum of two numbers is 13 and the sum of their square is 85. Find the numbers?
6 & 7 | |
B | 5 & 8 |
4 & 9 | |
D | 3 & 10 |
Question 4 Explanation:
Let the numbers be x and 13-x Then x^{2} + (13 – x)^{2} = 85 ∴ x^{2} + 169 + x^{2} – 26x = 85 ∴ 2 x^{2} – 26x + 84 = 0 ∴ x^{2} – 13x + 42 = 0 ∴ (x-6)(x-7)=0 Hence numbers are 6 & 7
- The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
4 | |
5 | |
C | 6 |
D | None of these |
Question 5 Explanation:
Let the ten's digit be x and unit's digit be y
Then (10x + y) – (10y + x) = 45
9(x – y) = 36
x – y = 4
Work and Wages
- Two friends A and B were employed to do a work. Initial deadline was fixed at 24 days. Both started working together but after 20 days, A left the work and the whole work took 30 days to complete. In how much time can B alone can do the work?
A | 40 |
B | 50 |
60 | |
70 |
Question 1 Explanation:
Let the total work be 24 units. It is given that A and B together can do the work in 24 days. => Combined efficiency of A and B = 24/24 = 1 unit / day => Work done in 20 days = 20 units => Work left = 24 – 20 = 4 units Now, this remaining 4 units of work was done by B alone in 10 days. => Efficiency of B = 4/10 = 0.4 Therefore, time required by B alone to do the work = 24/0.4 = 60 days
- A and B took a job to be completed in 20 days. They started working together and after 12 days, C joined them and the whole job finished in 15 days. How much time would C require to complete the job if only C was hired?
A | 15 |
12 | |
C | 10 |
D | 8 |
Question 2 Explanation:
Let the total job be 20 units. It is given that A and B took the job to be completed in 20 days. => Combined efficiency of A and B = 20/20 = 1 unit / day Now, job done in 12 days = 12 units => Job Left = 8 units Now, this remaining 8 units of job has been done by all A, B and C together. Let the efficiency of C be 'x'. => Combined efficiency of A, B and C = 1+x units/ day Now, with this efficiency, the job got completed in 3 more days. => Job done in 3 days = 3 x (1+x) = 8 units => x = 5/3 Therefore, efficiency of C = x = 5/3 units / day Hence, time required by C alone to do the job = 20/(5/3) = 12 days
- Three people A, B and C working individually can finish a job in 10, 12 and 20 days respectively. They decided to work together but after 2 days, A left the work and after another one day, B also left work. If they got two lacs collectively for the entire work, find the difference of the highest and lowest share.
70000 | |
60000 | |
C | 10000 |
D | 20000 |
Question 3 Explanation:
Let the total work be LCM(10, 12, 20) = 60 units => Efficiency of A = 60/10 = 6 units / day => Efficiency of B = 60/12 = 5 units / day => Efficiency of C = 60/20 = 3 units / day Since the number of working days are different for each person, the share of each will be calculated in the ratio of the units of work done. Now, A works for 2 days and B works for 3 days. => Work done by A = 2 x 6 = 12 units => Work done by B = 3 x 5 = 15 units => Work done by C = 60 – 12 – 15 = 33 units Therefore, ratio of work done = 12:15:33 = 4:5:11 So, A's share = (4/20) x 2,00,000 = Rs 40,000 B's share = (5/20) x 2,00,000 = Rs 50,000 C's share = (11/20) x 2,00,000 = Rs 1,10,000 Therefore, difference of the highest and lowest share = Rs 1,10,000 – 40,000 = Rs 70,000
- A alone and B alone can do a work in respectively 18 and 8 days more than both working together. Find the number of days required if both work together.
12 | |
B | 8 |
16 | |
D | 36 |
Question 4 Explanation:
Let the time required to complete the work by A and B together = n days => Time required by A alone = n + 18 days => Time required by B alone = n + 8 days Therefore, n^{2} = 18 x 8 = 144 => n = 12 Hence, A and B require 12 days to complete the work if they work together.
- Three friends A, B and C are employed to make pastries in a bakery. Working individually, they can make 60, 30 and 40 pastries respectively in an hour. They decided to work together but due to lack of resources, they had to work on shifts of 30 minutes. Find the time taken to make 185 pastries.
A | 4 hours |
3 hours 45 minutes | |
4 hours 15 minutes | |
D | 5 hours |
Question 5 Explanation:
It is given that A, B and C make 60, 30 and 40 pastries respectively in an hour. => In 30 minutes, they will make 30, 15 and 20 pastries respectively. So, in one cycle of 1 hour 30 minutes where each works for 30 minutes, pastries made = 30 + 15 + 20 = 65 Now, in 2 cycles (3 hours), 130 pastries would be made. In the next 30 minutes, A would make 30 pastries. So, total time elapsed = 3 hours 30 minutes and pastries made = 130 + 30 = 160 In the next 30 minutes, B would make 15 pastries. So, total time elapsed = 4 hours and pastries made = 160 + 15 = 175 In the next 15 minutes, C would make 10 pastries. So, total time elapsed = 4 hours 15 minutes and pastries made = 175 + 10 = 185 Therefore, total time taken = 4 hours 15 minutes
Pipes and Cisterns
- Two outlet pipes A and B are connected to a full tank. Pipe A alone can empty the tank in 10 minutes and pipe B alone can empty the tank in 30 minutes. If both are opened together, how much time will it take to empty the tank completely?
A | 7 minutes |
7 minutes 30 seconds | |
C | 6 minutes |
D | 6 minutes 3 seconds |
Question 1 Explanation:
Let the capacity of the tank be LCM(10, 30) = 30 units. => Efficiency of pipe A = 30 / 10 = 3 units / minute => Efficiency of pipe A = 30 / 30 = 1 units / minute => Combined efficiency of pipe A and pipe B = 4 units / minute Therefore, time required to empty the tank if both pipes work = 30 / 4 = 7 minutes 30 seconds
- Two pipes X and Y attached to a swimming pool can fill the pool in 20 minutes and 30 minutes respectively working alone. Both were opened together but due to malfunctioning of motor of pipe X, it had to be shut down after two minutes but Y continued to work till the swimming pool was filled completely. Find the total time taken to fill the pool.
27 | |
22 | |
C | 25 |
D | 20 |
Question 2 Explanation:
Let the capacity of the pool be LCM(20, 30) = 60 units. => Efficiency of pipe X = 60 / 20 = 3 units / minute => Efficiency of pipe Y = 60 / 30 = 2 units / minute => Combined efficiency of pipe X and pipe Y = 5 units / minute Now, the pool is filled with the efficiency of 5 units / minute for two minutes. => Pool filled in two minutes = 10 units => Pool still empty = 60 – 10 = 50 units This 50 units is filled by Y alone. => Time required to fill these 50 units = 50 / 2 = 25 minutes Therefore, total time required to fill the pool = 2 + 25 = 27 minutes
- Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively.After 4 minutes of working together, A got blocked and after another 1 minute, B also got blocked. C continued to work till the end and the cistern got completely filled. What is the total time taken to fill the cistern ?
A | 6 minutes |
B | 6 minutes 15 seconds |
6 minutes 40 seconds | |
D | 6 minutes 50 seconds |
Question 3 Explanation:
Let the capacity of the cistern be LCM(12, 15, 20) = 60 units. => Efficiency of pipe A = 60 / 12 = 5 units / minute => Efficiency of pipe B = 60 / 15 = 4 units / minute => Efficiency of pipe C = 60 / 20 = 3 units / minute => Combined efficiency of pipe A, pipe B and pipe C = 12 units / minute Now, the cistern is filled with the efficiency of 12 units / minute for 4 minutes. => Pool filled in 4 minutes = 48 units => Pool still empty = 60 – 48 = 12 units Now, A stops working. => Combined efficiency of pipe B and pipe C = 7 units / minute Now, the cistern is filled with the efficiency of 7 units / minute for 1 minute. => Pool filled in 1 minute = 7 units => Pool still empty = 12 – 7 = 5 units Now, B also stops working. These remaining 5 units are filled by C alone. => Time required to fill these 5 units = 5 / 3 = 1 minute 40 seconds Therefore, total time required to fill the pool = 4 minutes + 1 minutes + 1 minute 40 seconds = 6 minutes 40 seconds
- Three pipes A, B and C are connected to a tank. Working alone, they require 10 hours, 20 hours and 30 hours respectively. After some time, A is closed and after another 2 hours, B is also closed. C works for another 14 hours so that the tank gets filled completely. Find the time (in hours) after which pipe A was closed.
A | 1 |
B | 1.5 |
2 | |
3 |
Question 4 Explanation:
Let the capacity of the tank be LCM (10, 20, 30) = 60 => Efficiency of pipe A = 60 / 10 = 6 units / hour => Efficiency of pipe B = 60 / 20 = 3 units / hour => Efficiency of pipe C = 60 / 30 = 2 units / hour Now, all three work for some time, say 't' hours. So, B and C work for 2 more hours after 't' hours and then, C works for another 14 hours. => Combined efficiency of pipe A, pipe B and pipe C = 11 units / hour => Combined efficiency of pipe B and pipe C = 5 units / hour So, we have 11 x t + 5 x 2 + 14 x 2 = 60 => 11 t + 10 + 28 = 60 => 11 t = 60 – 38 => 11 t = 22 => t = 2 Therefore, A was closed after 2 hours.
- Working alone, two pipes A and B require 9 hours and 6.25 hours more respectively to fill a pool than if they were working together. Find the total time taken to fill the pool if both were working together.
A | 6 |
6.5 | |
C | 7 |
7.5 |
Question 5 Explanation:
Let the time taken if both were working together be 'n' hours. => Time taken by A = n + 9 => Time taken by B = n + 6.25 In such kind of problems, we apply the formula : n^{2} = a x b, where 'a' and 'b' are the extra time taken if both work individually than if both work together. Therefore, n^{2} = 9 x 6.25 => n = 3 x 2.5 = 7.5 Thus, working together, pipes A and B require 7.5 hours.
Percentages
- John earns 33.33% more than Peter. By what percentage is Peter's earning less than that of John's?
22 % | |
25 % | |
C | 26 % |
D | 23 % |
Question 1 Explanation:
Let John's income be j and Peter's income be p. Then, j = p + p × 33.33% = p + p × 100⁄3 % = p + p × 1/3 = 4p/3 ⇒ p = 3j/4 = (4 – 1)j/4 = j – j/4 = j – j × 1/4 = j – j × 100⁄4 % = j – j × 25%. Therefore, Peter's earning is less than John's earning by 25%.
- Mary's salary is reduced by 10%. By what percentage must her new salary be increased in order to gain her old salary?
A | 137⁄9 % |
B | 194⁄9 % |
100/9 % | |
D | 110⁄9 % |
Question 2 Explanation:
Let her old salary be Rs 100. Then, her new salary = 100 – 10 = Rs 90. So, to gain her old salary, her new salary must be increased by Rs 10. Therefore, the required percentage = (10⁄90) × 100% = 100/9 %.
- The price of sugar is decreased by 10%. As a consequence, monthly sales is increased by 30%. Find out the percentage increase in monthly revenue.
17 % | |
B | 19 % |
C | 18 % |
D | None of these |
Question 3 Explanation:
Let the price of sugar be Rs 100 and monthly sales be 100 units. Then, total revenue = 100 × 100 = Rs 10000. And, new revenue = 90 × 130 = Rs 11700. Increase in revenue = 11700 – 10000 = Rs 1700. Hence, percentage increase in revenue = (1700/10000) × 100% = 17%.
- Jack consumes 75% of his salary. Later his salary is increased by 20% and he increases his expenditures by 10%. Find the percentage increase in his savings.
A | 51% |
B | 60% |
50% | |
D | 55% |
Question 4 Explanation:
Let Jack's original salary be Rs 100. Then, his expenditure = Rs 75, his savings = Rs 25. Now, his new salary = Rs 120. So, new expenditure = (110/100) × 75 = Rs 165/2, new savings = 120 – 165/2 = Rs 75/2. Increase in savings = 75/2 – 25 = Rs 25/2. Therefore, percentage increase in savings = (25/2)/25 × 100% = 50%.
- Mary buys an item at Rs 25 in a sale and saves Rs 5. Find out the percentage of her savings.
A | 40/3 % |
B | 55/3 % |
50/3 % | |
None of these |
Question 5 Explanation:
Original Price of the item = 25 + 5 = Rs 30. Hence, the required percentage = (5/30) × 100% = 50/3 %.