Arithmetic (UPSC) Part- IV

21. If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure? [2020-II]

(a) 0.05 foot
(b) 0.25 foot
(c) 1 foot
(d) 3.25 feet

Correct Answer: (b) 0.25 foot

Solution:Let AB and CD are two straight sticks of length 7.5 feet and 3.25 feet respectively. If we cut the AB into 4 equal parts.

22. A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence? [2020-II]

(a) 34
(b) 36
(c) 38
(d) 40

Correct Answer: (c) 38

Solution:

Hence, next term of the series is 38.

23. Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D? [2020-II]

(a) 1
(b) 2
(c) 3
(d) 4

Correct Answer: (a) 1

Solution:Sum of numbers are:

Here, C + F = 12 (since 2 is at unit place of the sum)
As all letters represents different value,
so, (C, F) ≠ (2, 3)

Now, possible values of (C, F) = (4, 8), (5, 7) …(i)
Again, B + 2 = 10 – 1 ⇒ B = 9 – 2 = 7 …(ii)
and, 3 + E = 9 – 1 ⇒ E = 8 – 3 = 5 …(iii)
A + D = 15 ⇒ 9 + 6 = 15 …(iv)

From (i), (ii) and (iii), (C, F) = (4, 8)
From (i), (ii), (iii) and (iv)

Thus, A – D = 9 – 6 = 3

24. Consider the following data: [2020-II]

	Average marks in English	Average marks in Hindi
Girls	9	8
Boys	8	7
Overall average marks	8.8	x

What is the value of x in the above table?

(a) 7.8
(b) 7.6
(c) 7.4
(c) 7.4

Correct Answer: (a) 7.8

Solution:

Let number of girls and boys are m and n respectively.
Then, total marks in English = (8.8) × (m + n)
∴ 9m + 8n = (8.8)(m + n)
⇒ 0.2m = 0.8n ⇒ m = 4n.

Again, total marks in Hindi = x(m + n)
⇒ 8m + 7n = x(m + n)
⇒ 8(4n) + 7n = x(4n + n)
⇒ 39n = 5n × x ⇒ x = 39/5 = 7.8

25. How many zeroes are there at the end of the following product? [2020-II]

1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60

(a) 10
(b) 12
(c) 14
(d) 15

Correct Answer: (c) 14

Solution:

Given product
1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60
= 1 × 5 × 10 × (15 × 2) × 10 × 25 × 30 × (35 × 2) × 10 × (2 × 45) × 50 × (55 × 2) × 30
= 1 × 5 × 10 × 30 × 10 × 25 × 30 × 70 × 10 × 90 × 50 × 110 × 30

Total number of zeroes = 10.

26. Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by [2020-II]

(a) 3
(b) 9
(c) 37
(d) (X + Y + Z)

Correct Answer: (b) 9

Solution:Here (x + y + z) is not divisible by 3.
So, number formed by the digits x, y and z will not be divisible by 3.
Number, xyz, yzx and zxy will not be divisible by 3.
Now, xyz + yzx + zxy = 3(x + y + z) will be divisible by 3 but not by 9.

27. Let p, q, r and s be natural numbers such that p – 2016 = q + 2017 = r – 2018 = s + 2019 Which one of the following is the largest natural number? [2020-II]

(a) p
(b) q
(c) r
(d) s

Correct Answer: (c) r

Solution:

28. How many pairs of natural numbers are there such that the difference of whose squares is 63? [2020-II]

(a) 3
(b) 4
(c) 5
(d) 2

Correct Answer: (a) 3

Solution:

29. Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6? [2020-II]

(a) 2/3
(b) 3/4
(c) 4/5
(d) 5/6

Correct Answer: (d) 5/6

Solution:

30. A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4? [2020-II]

(a) 2n
(b) 3n
(c) 2n + 4
(d) 3n + 1

Correct Answer: (d) 3n + 1

Solution:n is a digit, which is divisible by 3 but not by 2.
∴ n = 9
Now, 2 × 9 = 18; 18 is not divisible by 4.
3 × 9 = 27; 27 is not divisible by 4.
2 × 9 + 4 = 22; 22 is not divisible by 4.
3 × 9 + 1 = 28; 28 is divisible by 4.

Arithmetic (UPSC) Part- IV

21. If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure? [2020-II]

22. A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence? [2020-II]

23. Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D? [2020-II]

24. Consider the following data: [2020-II]

25. How many zeroes are there at the end of the following product? [2020-II]

26. Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by [2020-II]

27. Let p, q, r and s be natural numbers such that p – 2016 = q + 2017 = r – 2018 = s + 2019 Which one of the following is the largest natural number? [2020-II]

28. How many pairs of natural numbers are there such that the difference of whose squares is 63? [2020-II]

29. Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6? [2020-II]

30. A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4? [2020-II]

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