Arithmetic (UPSC) Part- II

Total Questions: 50

11. There are 240 balls and n number of boxes B₁, B₂, B₃, ... Bₙ. The balls are to be placed in the boxes such that B₁ should contain 4 balls more than B₂, B₂ should contain 4 balls more than B₃, and so on. Which one of the following cannot be the possible value of n? [2009]

(a) 4
(b) 5
(c) 6
(d) 7

Correct Answer: (d) 7

Solution:Since, common difference between no.of balls in box is 4, so it can be taken as an A.P. series.

n[2a+(n−1)4]=480⇒2a−(n−1)4=480/n

As L.H.S of this equation given an integer value so R.H.S must be an integer and thus 480 should be divisible by $n$ . Out of the given options, 480 is not divisible by 7 only.

12. In a tournament 14 teams play league/matches. If each team plays against every other team only once then how many matches are played? [2010]

(a) 105
(b) 91
(c) 85
(d) 78

Correct Answer: (c) 85

Solution:

1st team can play with rest of the 13, 2nd team can play with the remaining 12 and so on.
Hence, total no. of matches = 13 + 12 + ... + 1

13. Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X? [2010]

(a) 8%
(b) 9%
(c) 10%
(d) 12%

Correct Answer: (c) 10%

Solution:Let value of

Z

be 100
Then,

X = Z - 20 = 100 - 20 = 80

∴

Hence, Y is 10% less than the number X.

14. How many numbers from 0 to 999 are not divisible by either 5 or 7? [2010]

(a) 313
(b) 341
(c) 686
(d) 786

Correct Answer: (c) 686

Solution:

Numbers from (0 – 999) divisible by 7,

Numbers from (0 – 999) divisible by 5,

999/5 = 199×4/5 ≈199

There are few numbers which are divisible by both 5 and 7, i.e., by 35.
Numbers from (0 – 999) divisible by 35,

199/35 =28 ×19/35 ≈ 28

Numbers divisible by 5 or 7 =
Hence, total numbers between (0 – 999) not divisible by 5 or 7 =

15. In a group of five persons A, B, C, D and E, there is a professor, a doctor and lawyer. A and D are unmarried ladies, and do not work. Of the married couple in the Group, E is the husband. B is the brother of A and is neither a doctor nor a lawyer. Who is the professor? [2010]

(a) B
(b) C
(c) A
(d) None of these

Correct Answer: (a) B

Solution:As A and D do not work, so any of B, C or E could be the professor, doctor or lawyer. Now, B is neither a doctor nor lawyer, so clearly B is the professor.

16. Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are below twenty five. Then, which one of the following is certainly true? [2010]

(a) All the villagers who have their own houses are literate
(b) Some villagers under twenty five are literate
(c) A quarter of the villagers who have their own houses cultivate paddy
(d) Half of the villagers who cultivate paddy are literate

Correct Answer: (b) Some villagers under twenty five are literate

Solution:

Let total number of villagers =

No. of villagers having own horse =

No. of villagers cultivating paddy =

No. of villagers that are literate =

No. of villagers that are below 25 =

All the villagers who have their own houses are 50, while no. of literate villagers are 33, so (a) is not true.

No. of villagers under 25 is 80, while literate are 33, so clearly some of them under 25 are literate.

Thus, option (b) is correct.
Similarly (c) and (d) also, are not true.

17. Each person’s performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons? [2010]

(a) 66
(b) 55
(c) 54
(d) 45

Correct Answer: (b) 55

Solution:

1st person is to be compared with the other 10 persons i.e., 10 comparisons.
2nd person is to be compared with the remaining 9 persons, and so on.

Hence, total no. of comparisons =

18. A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4th full? [2010]

(a) 6
(b) 12
(c) 17
(d) 22

Correct Answer: (d) 22

Solution:

Let $x$ be the number of eggs already present in the basket.
Then, the number of eggs on each successive day:

On the 24th day, the basket was filled completely

on the 23rd day, the basket was filled =

Hence, on the 22nd day, the basket was filled =

19. The difference between the simple interest received from two banks on ₹500 for two years is ₹2.50. What is the difference between their rates? [2010]

(a) 0.25%
(b) 0.5%
(c) 1%
(d) 2.5%

Correct Answer: (a) 0.25%

Solution:

20. A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test? [2010]

(a) 36
(b) 30
(c) 25
(d) 20

Correct Answer: (d) 20

Solution:

Let total number of questions =
Now, right questions = 12 = 60% of

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Arithmetic (UPSC) Part- II

11. There are 240 balls and n number of boxes B₁, B₂, B₃, ... Bₙ. The balls are to be placed in the boxes such that B₁ should contain 4 balls more than B₂, B₂ should contain 4 balls more than B₃, and so on. Which one of the following cannot be the possible value of n? [2009]

12. In a tournament 14 teams play league/matches. If each team plays against every other team only once then how many matches are played? [2010]

13. Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X? [2010]

14. How many numbers from 0 to 999 are not divisible by either 5 or 7? [2010]

15. In a group of five persons A, B, C, D and E, there is a professor, a doctor and lawyer. A and D are unmarried ladies, and do not work. Of the married couple in the Group, E is the husband. B is the brother of A and is neither a doctor nor a lawyer. Who is the professor? [2010]

16. Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are below twenty five. Then, which one of the following is certainly true? [2010]

17. Each person’s performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons? [2010]

18. A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4th full? [2010]

19. The difference between the simple interest received from two banks on ₹500 for two years is ₹2.50. What is the difference between their rates? [2010]

20. A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test? [2010]

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