**Q1. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:**

(a) 308

(b) 125

(c) 274

(d) 29

**Q3. What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case?**

(a) 30

(b) 31

(c) 32

(d) 34

**Q4. What is the sum of the digits of the least number which when divided by 54 leaves 35 as remainder, when divided by 80 leaves 61 as remainder and when divided by 119 leaves 100 as remainder?**

(a) 21

(b) 19

(c) 25

(d) 28

**Q5. If a^2-4a-1 = 0, then value of a^2+1/a^2 +3a-3/a is**

(a) 25

(b) 30

(c) 35

(d) 40

**Q6. In a family of 5 members, the average age at present is 33 years. They youngest member is 9 years old. The average age of the family just before the birth of the youngest member was**

(a) 30 years

(b) 29 years

(c) 25 years

(d) 24 years

**Q7. The mean of 100 items was 46. Later, it was discovered that an item 16 was misread as 61 and another item 43 was misread as 34. It was also found that the number of items was 90 and not 100. Then what is the correct mean?**

(a) 50

(b) 50.7

(c) 52

(d) 52.7

**Q8. In an examination, 10% of the students failed in Physics, 20% failed in Chemistry and 5% failed in both. What is the percentage of students who failed in at least one subject?**

(a) 23%

(b) 75%

(c) 34%

(d) 67%

**Q9. In an examination, it is required to get 296 marks out of aggregate marks to pass. A student gets 222 marks and is declared failed by 10% marks. What are the maximum aggregate marks as student can get?**

(a) 830

(b) 810

(c) 780

(d) 740

**Q10. Anupam purchased 5 Lemons for Rs. 4. He sold all the Lemons and earned 75% Profit. At what rate did he sell the Lemons?**

(a) 1.4

(b) 9

(c) 3.2

(d) 3

**Solutions:**

S1. Ans.(a)

Sol. Let the other number be x. Then,

11 × 7700 = 275 × x

⇒x=(11×7700)/275=308

Hence, the other number is 308.

S3. Ans.(c)

Sol. The required greatest number is the HCF (263 – 7, 935 – 7, 1383 – 7)

i.e., HCF OF 256, 928 and 1376

HCF = 32

S4. Ans.(d)

Sol. (54 – 35) = 19, (80 – 61)

= 19 and (119 – 100) = 19

LCM of 54, 80 and 119 is 257040.

Required least number = 257040 + 19 = 257059

Sum of the digits of 257059 = 2 + 5 + 7 + 0 + 5 + 9 = 28

S6. Ans.(a)

Sol. Sum of the present age of family members

= 33 × 5 = 165 years

9 years ago,

Sum of their ages = 165 – 9 × 5 = 120 years

∴ Required average age = 120/4 = 30 years

S7. Ans.(b)

Sol. Required Average

=(100×46-61-34+16+43)/90

=(4600-36)/90=4564/90=50.7

S9. Ans.(d)

Sol. Let the maximum aggregate marks be x.

According to the question,

10% of x = 296 – 222

⇒x/10=74

⇒ x = 74 ×10 = 740

S10. Ans.(a)

Sol. Directly: Cost price for 5 Lemon is Rs. 4

So, SP for 5 Lemon = 4 × ((100 + 75))/100 = Rs. 7

So, SP for 1 Lemon = 7/5 = Rs. 1.4