Arithmetic (UPSC) Part- II

Total Questions: 50

1. In the series [2008]

1 2 3 4 5

A AB ABC ABCD ABCDE...
Which letter occupies the 100th position?

(a) H
(b) I
(c) J
(d) K

Correct Answer: (b) I

Solution:

Given series contains 1, 2, 3, 4 .......... alphabets from the beginning. So upto 13th term, number of alphabets $= 13 ( 13 + 1 ) = 91$

Again it will start from alphabet A and thus 100th alphabet will be I.

2. What is the number of terms in the series 117, 120, 123, 126, ..., 333? [2008]

(a) 72
(b) 73
(c) 76
(d) 79

Correct Answer: (b) 73

Solution:

117, 120, 123, 126, \dots\dots\dots, 333

Given series is an A.P. series with first term,

$a = 117$ , last term $l = 333$ and common difference, $d = 3$ last term, $l = a + (n - 1) d$ where, $n =$ number of terms.

$117 + (n - 1) 3 = 333$ $(n - 1) 3 = 216 \Rightarrow n = 73$

3. A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is ₹600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%? [2008]

(a) ₹802.50
(b) ₹811.25
(c) ₹862.50
(d) ₹875

Correct Answer: (c) ₹862.50

Solution:Cost price = Money spent by the person to purchase + selling expenses

600 + (600 × 15/100) = 690

Hence, selling price $= 690 (1 + 25) = 862.50$

4. In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II. 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of students? [2008]

(a) 600
(b) 580
(c) 560
(d) 540

Correct Answer: (a) 600

Solution:

% of students failed in paper I $= 100 - 70 = 30%$

% of students failed in paper II $= 100 - 60 = 40%$

total % of students who failed $= 30 + 40 - 15 = 55%$

total % of students who passed in both papers $100 - 55 = 45%$

Let, total number of students be $x$ .

Now, $45%$ of $x = 270$

$45 \times x = 270 \Rightarrow x = 600$

5. March 1, 2008 was Saturday. Which day was it on March 1, 2002? [2008]

(a) Thursday
(b) Friday
(c) Saturday
(d) Sunday

Correct Answer: (b) Friday

Solution:

In a year, number of weeks $= 52$

extra day $= 1$

From 2002 to 2008, there are 6 years.

So number of extra days $= 6 (1) = 6$

While 2004 and 2008 are leap years, having one more extra day apart from the normal extra day.

Thus, number of extra days $= 6 + 1 + 1 = 8$

Out of these 8 extra days, 7 days form a week and so 1 day remains.

Hence, March 1, 2002 is 1 day less then March 1, 2008 i.e., it is Friday.

6. There are four persons A, B, C, D; and A has some coins. A gave half of the coins to B and 4 more besides. B gave half of the coins to C and 4 more besides. C gave half of the coins to D and 4 more besides. Both B and D end up with same number of coins. How many coins did A have originally? [2009]

(a) 96
(b) 84
(c) 72
(d) 64

Correct Answer: (c) 72

Solution:Let A contains

x

coins.

B = x + 4, C = 1 (x/2 + 4) + 4

= 1/2(x/2+4) − 4 =x/4 - 2

D = 1/2 [1/2 (x/2 + 4) + 4] + = x/8 + 7

8x = 9, x = 72

7. While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed? [2009]

(a) 11
(b) 12
(c) 13
(d) 14

Correct Answer: (c) 13

Solution:Let there be n natural numbers and 'x' be the number missed out.

$n ( n + 1 )/2 - x = 177$

$n (n + 1) - 2 x = 354 \Rightarrow n (n + 1) = 354 + 2 x$

Out of the given options only $x = 13$ satisfies it, as $19$ $(19 + 1) = n (n + 1) = 354 + 2 (13) = 380$

8. Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut? [2009]

(a) 27
(b) 36
(c) 43
(d) 400

Correct Answer: (b) 36

Solution:Since each rod must be cut into parts of equal length and each part must be as long as possible, so HCF should be taken.

HCF of 78, 104, 117 and 169 $= 13$ .

No. of parts from 78cm. rod= 78/13 = 6

No. of parts from 104 cm. rod = 104/13 = 8

No. of parts from 117 cm. rod = 117/13

No. of parts from 169 cm. rod = 169/13 = 13.

$∴$ Maximum no. of pieces $= 6 + 8 + 9 + 13 = 36$

9. In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed in A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between [2009]

(a) 42% and 84%
(b) 42% and 78%
(c) 58% and 78%
(d) 58% and 84%

Correct Answer: (a) 42% and 84%

Solution:Pass % is minimum when failure % is maximum.

Maximum % of failure $= 20 + 22 + 16 = 58%$

$∴$ Minimum pass % $= 100 - 58 = 42%$

Now, pass % is maximum, when failure % is minimum. Minimum % of failure $= 16%$

$(∵ 22%$ failure covers both $16%$ and $20%$ i.e., $22%$ is the minimum value of failure $%)$ .

$∴$ Maximum % of passing $= 100 - 16 = 84%$

Hence, pass % range $= 42%$ to $84%$ .

10. How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.? [2009]

(a) 9
(b) 10
(c) 18
(d) 20

Correct Answer: (c) 18

Solution:In one hour, hour hand and minute hand are at right angles 2 times.

Time $= 10$ p.m $- 1$ p.m $= 9$ hr.

$∴$ No. of times, when both hands are perpendicular to each other in 9 hr $= 9 \times 2 = 18$

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Arithmetic (UPSC) Part- II

1. In the series [2008]

2. What is the number of terms in the series 117, 120, 123, 126, ..., 333? [2008]

3. A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is ₹600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%? [2008]

4. In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II. 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of students? [2008]

5. March 1, 2008 was Saturday. Which day was it on March 1, 2002? [2008]

7. While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed? [2009]

8. Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut? [2009]

9. In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed in A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between [2009]

10. How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.? [2009]

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