Arithmetic (UPSC) Part- IV

Total Questions: 50

11. Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena’s father get married? [2019-II]

(a) 22 years
(b) 23 years
(c) 24 years
(d) 25 years

Correct Answer: (b) 23 years

Solution:Mother is 24 years older than Ena.
So, at the time of Ena’s birth, mother's age was 24 years.
Again, Ena was born after 4 years of their parents' wedding.

So, mother's age at the time of wedding
= 24 – 4 = 20 years
Her father is 3 years older than her mother
So, her father's age at the time of their wedding
= 20 + 3 = 23 years.

12. Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered? [2019-II]

(a) 15%
(b) 20%
(c) 25%
(d) 30%

Correct Answer: (b) 20%

Solution:

Let price of each mobile is ₹1000.
Then, Price of 8 mobiles = ₹8000.
Price of 10 mobiles = ₹10000.

13. The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are [2019-II]

(a) 39
(b) 39.7
(c) 40
(d) 40.3

Correct Answer: (b) 39.7

Solution:

Total marks of 100 students = $40 \times 100 = 4000$
Correct mean marks of 100 students =

14. Two Statements are given followed by two Conclusions: [2020-II]

Statements:
All numbers are divisible by 2.
All numbers are divisible by 3.
Conclusion-I: All numbers are divisible by 6.
Conclusion-II: All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?

(a) Only Conclusion-I
(b) Only Conclusion-II
(c) Neither Conclusion-I nor Conclusion-II
(d) Both Conclusion-I Conclusion-II

Correct Answer: (a) Only Conclusion-I

Solution:

I. Numbers divisible by 2 are 2, 4, 6, 8, 10, ...
II. Numbers divisible by 3 are 3, 6, 9, 12, ...
Thus, numbers divisible by both 2 and 3 are 6, 12, 18, 24, ...

Conclusion I: Number divisible by 6 are 6, 12, 18, 24, ...
Hence, conclusion I is true.

Conclusion II: Numbers divisible by 4 are 4, 8, 12, 16, ...
Here 6, 18, 30, ... are not divisible by 4 but divisible by 2 and 3.
Hence, conclusion II is not correct.

15. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4? [2020-II]

(a) 5
(b) 11
(c) 12
(d) 13

Correct Answer: (c) 12

Solution:Between 1 to 100, there are 12 integer numbers that have 4 as a digit but are not divisible by 4. Those numbers are:
14, 34, 41, 42, 43, 45, 46, 47, 49, 54, 74, and 94.

16. The average age are of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher? [2020-II]

(a) 25 years
(b) 30 years
(c) 35 years
(d) 45 years

Correct Answer: (c) 35 years

Solution:

17. A person bought a car and sold it for ₹3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car? [2020-II]

(a) ₹3,60,000
(b) ₹3,65,000
(c) ₹3,70,000
(d) ₹3,75,000

Correct Answer: (d) ₹3,75,000

Solution:

18. Two Statements S1 and S2 are given below followed by a Question: [2020-II]

S1: n is a prime number.
S2: n leaves a remainder of 1 when divided by 4.

Question:

If n is a unique natural number between 10 and 20, then what is n?
Which one of the following is correct in respect of the above Statements and the Question?

(a) S1 alone is sufficient to answer the Question.
(b) S2 alone is sufficient to answer the Question.
(c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
(d) S1 and S2 together are not sufficient to answer the Question.

Correct Answer: (d) S1 and S2 together are not sufficient to answer the Question.

Solution:

19. Two Statements S1 and S2 are given below with regard to two numbers followed by a Question: [2020-II]

S1: Their product is 21.
S2: Their sum is 10.
Question: What are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?

(a) S1 alone is sufficient to answer the Question.
(b) S2 alone is sufficient to answer the Question.
(c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
(d) S1 and S2 together are not sufficient to answer the Question.

Correct Answer: (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

Solution:

20. In the sum [2020-II]

⊗ + 1 × ⊗ + 5 × ⊗ + ⊗ × ⊗ + ⊗ + ⊗ + ⊗ + 1 = 1 ⊗ ⊗
for which digit does the symbol ⊗ stand?

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

Correct Answer: (b) 3

Solution:

For $x = 3$

In such type of question, we check the solutions by going through the given options.

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Arithmetic (UPSC) Part- IV

11. Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena’s father get married? [2019-II]

12. Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered? [2019-II]

13. The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are [2019-II]

14. Two Statements are given followed by two Conclusions: [2020-II]

15. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4? [2020-II]

16. The average age are of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher? [2020-II]

17. A person bought a car and sold it for ₹3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car? [2020-II]

18. Two Statements S1 and S2 are given below followed by a Question: [2020-II]

19. Two Statements S1 and S2 are given below with regard to two numbers followed by a Question: [2020-II]

20. In the sum [2020-II]

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