Arithmetic (UPSC) Part- V

Total Questions: 50

21. A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two digit number. How many coins does A have in the beginning? [2022-II]

(a) 76
(b) 68
(c) 60
(d) 52

Correct Answer: (d) 52

Solution:Number of coins D have = 10 (smallest 2-digits number)

Number of coins C have = (10 – 2) × 2 = 16
Number of coins B have = (16 – 2) × 2 = 28
Number of coins A have = (28 – 2) × 2 = 52

22. How many seconds in total are there in x weeks, x days, x hours, x minutes and seconds? [2022-II]

(a) 11580x
(b) 11581x
(c) 694860x
(d) 694861x

Correct Answer: (b) 11581x

Solution:Total seconds
= {(7x + x) × 24 + x} × 3600 + x × 60 + x
= 694861x seconds.

23. Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below: [2022-II]

Z purchased 8 notebooks more than X did.
P and Q together purchased 21 notebooks.
Q purchased 5 notebooks less than P did.
X and Y together purchased 28 notebooks.
P purchased 5 notebooks more than X did.
If each notebook is priced ₹40, then what is the total cost of all the notebooks?

(a) ₹2,600
(b) ₹2,400
(c) ₹2,360
(d) ₹2,320

Correct Answer: (a) ₹2,600

Solution:From given information 1 to 5, we get
that (i) z = x + 8, (ii) P + Q = 21
(iii) Q = P – 5 (iv) x + y = 28
(v) P = x + 5
From (ii) + (iii), 2Q = 16
⇒ Q = 8 and P = 8 + 5 = 13
From (v), 13 = x + 5
⇒ x = 8
From (iv), 8 + y = 28
⇒ y = 20
From (i), z = 8 + 8 = 16
Total cost = (P + Q + X + Y + Z) × 40
= (13 + 8 + 8 + 20 + 16) × 40 = 2600

24. A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number? [2022-II]

(a) 147
(b) 150
(c) 294
(d) 300

Correct Answer: (c) 294

Solution:L.C.M of 2, 3, 4, 5 and 6 = 60
Now, A must have pens in mutiple of 60.

For A = 60 pens, D = 60/4 = 15 pens, which is odd

For A = 120 pens, B = 120/2 = 60 ,
C = 120/3 = 40
D = 120/4 = 30 , E = 120/5 = 24 , F = 120/6 = 20
Total pens = 120 + 60 + 40 + 30 + 24 + 20 = 294

25. Consider the Question and two Statements given below: [2022-II]

Question: What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother
Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.
Which one of the following is correct in respect of the question and the statements?

(a) Statement-1 alone is sufficient to answer the question.
(b) Statement-2 alone is sufficient to answer the question.
(c) Both statement-1 and statement-2 are sufficient to answer the question.
(d) Both statement-1 and statement-2 are not sufficient to answer the question.

Correct Answer: (c) Both statement-1 and statement-2 are sufficient to answer the question.

Solution:From statement 1 and 2 together
5 years later Manisha's age = 3x
Mother's age = 5x
Again, (5x – 5) – (3x – 5) = 24
x = 12

Hence, Manisha's present age = 3x – 5
= 36 – 5 = 31 years
Hence, both statement 1 and 2 required together to answer the question

26. Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements: [2022-II]

The 4-digit least value of x is 1332.
The 3-digit greatest value of x is 888.
Which of the above statements is/are correct?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Correct Answer: (a) 1 only

Solution:Total number of 3 digits number from digit A, B and
C = 3! = 6

Now, sum X = ABC + ACB + BCA + BAC + CAB + CBA
= 2(A + B + C), 2(A + B + C), 2(A + B + C)
For minimum value of X, let A = 1, B = 2, C = 3
X = 2(1 + 2 + 3), 2(1 + 2 + 3), 2(1 + 2 + 3)
= (12 + 1), (12 + 1), 2 = 1332
This is minimum value of x

27. What is the remainder when [2022-II]

91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?

(a) 3
(b) 2
(c) 1
(d) 0

Correct Answer: (d) 0

Solution:1261 = 13 × 97
Now, (91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99) is completely divisible by 1261
Hence, remainder = 0

28. When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct? [2022-II]

(a) z < x < y
(b) x < y < z
(c) y < x < z
(d) z < y < x

Correct Answer: (d) z < y < x

Solution:0.7x + y = 1.65 y
⇒ 0.7x = 0.65y
14x = 13y
∴ x = 13/14 y .......... (i)

and, 0.6x + z = 1.65z
⇒ 0.6x = 0.65z
12x = 13z
x = 13/12 z .......... (ii)
From (i) and (ii) we get
x = 13/14 y = 13/12 z
∴ y > x > z

29. Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list? [2022-II]

(a) 15000
(b) 12000
(c) 9600
(d) 5000

Correct Answer: (a) 15000

Solution:Total number of vote cost = N
56% of N – (100 – 56)% of N = 1440
12% of N = 1440
N = (1440 × 100) / 12 = 12000
∴ Total number of votes in the votes lists
= 12000 × (100 / 80) = 15000

30. What is the smallest number greater than 1000 that when divided by anyone of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3? [2022-II]

(a) 1063
(b) 1073
(c) 1083
(d) 1183

Correct Answer: (c) 1083

Solution:L.C.M of 6, 9, 12, 15 and 18 = 180.
Smallest number (>1000) completely divisible by 180 = 1080
Remainder = 3
Hence, required number = 1080 + 3 = 1083

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