**Q1. If the number 97215X6 is completely divisible by 11, then the smallest whole number in place of X will be: **

(a) 3

(b) 2

(c) 1

(d) 5

**S1. Ans.(a)**

**Sol. **Given number = 97215×6

(6 + 5 + 2 + 9) – (x + 1 + 7) = (14 – x), which must be divisible by 11.

∴ x = 3.

**Q2. If the number 91876X2 is completely divisibly by 8, then the smallest whole number in place of X will be: **

(a) 1

(b) 2

(c) 3

(d) 4

**S2. Ans.(c)**

**Sol**. The number 6×2 must be divisible by 8.

∴ x = 3, as 632 is divisible by 8.

**Q3. If x and y are the two digits of the number 653 xy such that this number is divisible by 80, then ****x + y = ? **

(a) 2

(b) 3

(c) 4

(d) 6

**S3. Ans.(a)**

**Sol. **80 = 2 × 5 × 8

Since 653 xy is divisible by 2 and 5 both, so y = 0

Now, 653 x0 is divisible by 8, so 3×0 should be divisible by 8. This happens when x = 2

∴ x + y = (2 + 0) = 2

**Q4. If the product 4864 × 9 P 2 is divisible by 12, the value of P is: **

(a) 2

(b) 5

(c) 6

(d) 1

**S4. Ans.(d)**

**Sol.** Clearly, 4864 is divisibly by 4.

So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.

∴ P = 1.

**Q5. On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5? **

(a) 0

(b) 1

(c) 2

(d) 4

**S5. Ans.(d)**

**Sol.** Let the number is=5x+3

Square of the number=(5x+3)^2

Remainder=9/5=4

**Q6. The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: **

(a) 3/5

(b) 3/10

(c) 4/5

(d) 5/4

**Q8. A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?**

(a) 10

(b) 11

(c) 12

(d) 15

**Q9. When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number? **

(a) 339

(b) 349

(c) 369

(d) Data inadequate

**S9. Ans.(b)
Sol.** x = 13p + 11 and x = 17q + 9

∴13p+11=17q+9⇒17q-13p=2⇒q=(2 + 13p)/17

The least value of p for which q=(2 + 13p)/17 is a whole number is p = 26

∴ x=(13×26+11)=(338+11)=349

**Q10. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:**

(a) 553681

(b) 555181

(c) 555681

(d) 556581

**S10. Ans.(c)**

**Sol.**987 = 3 × 7 × 47

So, the required number must be divisible by each one of 3, 7, 47

553681 → (Sum of digits = 28, not divisible by 3)

555181 → (Sum of digits = 25, not divisible by 3)

555681 is divisible by each one of 3, 7, 47.

**Q12. Three numbers are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is: **

(a) 75

(b) 81

(c) 85

(d) 89

**S12. Ans.(c)**

**Sol.** Since the numbers are co-prime, they contain only 1 as the common factor.

Also, the given two products have the middle number in common

So, middle number = H.C.F of 551 and 1073 = 29;

First number =(551/29)=19; Third number =(1073/29)=37

∴ Required sum = (19 + 29 + 37) = 85.

**Q13. Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly? **

(a) 1 litre

(b) 7 litres

(c) 31 litres

(d) 41 litres

**S13. Ans.(c)**

**Sol. **Required measurement = (H.C.F of 496, 403, 713) litres = 31 litres

**Q14. The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case, is: **

(a) 64

(b) 124

(c) 156

(d) 260

**S14. Ans.(a)**

**Sol. **Required number = H.C.F of (1356 – 12), (1868 – 12) and (2764 – 12)

= H.C.F of 1344, 1856 and 2752 = 64.

**Q15. The least number, which when divided by 48, 60, 72, 108 and 140 leaves 38, 50, 62, 98 and 130 as remainders respectively, is: **

(a) 11115

(b) 15110

(c) 15120

(d) 15210

**S15. Ans.(b)**

**Sol. **Here (48 – 38) = 10, (60 – 50) = 10, (72 – 62) = 10, (108 – 98) = 10 & (140 – 130) = 10

∴ Required number = (L.C.M of 48, 60, 72, 108, 140) – 10 = 15120 – 10 = 15110.