**Q1.**

Find the greatest number which divides the number 1461, 4185 and 4227 leaving

remainders 2, 3 and 4, respectively.

Find the greatest number which divides the number 1461, 4185 and 4227 leaving

remainders 2, 3 and 4, respectively.

(a)

43

43

(b)

41

41

(c)

48

48

(d)

None of these

None of these

S1. Ans.(b)

Sol. Greatest number which divides the

numbers 4061, 4185 and 4227 leaving remainders 2, 3 and 4 will be equal to HCF

of (4061 – 2), (4185 – 3), (4227 – 4) i.e. HCF of 4059, 4182 and 4223.

numbers 4061, 4185 and 4227 leaving remainders 2, 3 and 4 will be equal to HCF

of (4061 – 2), (4185 – 3), (4227 – 4) i.e. HCF of 4059, 4182 and 4223.

Since, HCF and 4059, 4182 and 4223 is 41.

So, the required number is 41.

So, the required number is 41.

**Q2.**

Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into

parts of equal length. Each part must be as long as possible. What is the

maximum number of pieces that can be cut?

Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into

parts of equal length. Each part must be as long as possible. What is the

maximum number of pieces that can be cut?

(a)

27

27

(b)

36

36

(c)

43

43

(d)

480

480

S2. Ans.(b)

Sol. Given, lengths of four metal rods are

78, 104, 117 and 169 cm.

78, 104, 117 and 169 cm.

Now, 78 = 13 × 2 × 3

104 = 13 × 2 × 2 × 2

117 = 13 × 3 × 3

169 = 13 × 13

Length of each piece of rod as possible.

HCF = 13 cm

∴ Number of pieces

= 6 + 8 + 9 + 13 = 36

= 6 + 8 + 9 + 13 = 36

**Q3.**

There are five hobby clubs in a college viz. photography, yachting, chess

electronics and gardening. The gardening group meets every second day, the

electronics group meets every third day, the chess group meets every fourth day,

the yachting group meets every fifth day and the photography group meets every

sixth day. How many times do all the five groups meet on the same day within

180 days?

There are five hobby clubs in a college viz. photography, yachting, chess

electronics and gardening. The gardening group meets every second day, the

electronics group meets every third day, the chess group meets every fourth day,

the yachting group meets every fifth day and the photography group meets every

sixth day. How many times do all the five groups meet on the same day within

180 days?

(a)

3

3

(b)

5

5

(c)

10

10

(d)18

S3. Ans.(a)

Sol. Gardening group meets once in 2 days, electronics group meets once in 3 days, chess group meets once in 4 days, yachting group meets once in 5 days and the photography group meets once in 6 days.

If they meet on the same day one time, then the next time they will meet on the same day again will be the LCM of 2, 3, 4, 5 and 6 which is equal of 60. Hence, within 180 days all the five groups will meet on the same day =180/60 = 3 times

Q4. What is the sum of digits of the least number, which when divided by 52

leaves 33 as remainder, when divided by 78 leaves 59 as remainder and when

divided by 177 leaves 98 as remainder?

Q4. What is the sum of digits of the least number, which when divided by 52

leaves 33 as remainder, when divided by 78 leaves 59 as remainder and when

divided by 177 leaves 98 as remainder?

(a)

21

21

(b)

27

27

(c)

19

19

(d)

36

36

S4. Ans.(c)

Sol. (52 – 33) = 19, (78 – 59) = 19 and

(117 – 98) = 19

(117 – 98) = 19

LCM of 52, 78 and 117 is 468.

Required least number = 468 + 19 = 487

Sum of digits of 487 = 4 + 8 + 7 = 19

**Q5.**

The product of two relatively prime numbers is 143. Find their HCF.

The product of two relatively prime numbers is 143. Find their HCF.

(a)

3

3

(b)

9

9

(c)

13

13

(d)

1

1

S5. Ans.(d)

Sol. Two divisible prime numbers are

exactly divisible by 1 only.

exactly divisible by 1 only.

∴ Required HCF = 1

**Q6. If (22) ^3 is subtracted from**

the square of a number, the answer so obtained is 9516. What is the number?

the square of a number, the answer so obtained is 9516. What is the number?

(a) 144

(b) 142

(c) 138

(d) 136

S6. Ans.(b)

Sol. Let the number be x.

Now, according to the question,

X^2 – (22) ^3 = 9516

or, x^2 = 9516 + (22) ^3 = 9516 + 10648 = 20164

x = √20164= 142

**Q7. A gardener plants 34969 mango**

trees in his garden and arranges them so that there are so many rows as there

are mango trees in each row. The number of rows is-

trees in his garden and arranges them so that there are so many rows as there

are mango trees in each row. The number of rows is-

(a) 187

(b) 176

(c) 169

(d) 158

S7. Ans.(a)

Sol. No of each rows is equal to the number of trees in each rows that means the number of rows and column is same = √34969

= 187

**Q8. Sum of eight consecutive numbers**

of Set A is 376. What is the sum of five consecutive numbers of another set if

its minimum number is 15 ahead of average of Set A?

of Set A is 376. What is the sum of five consecutive numbers of another set if

its minimum number is 15 ahead of average of Set A?

(a) 296

(b) 320

(c)284

(d)324

(b) 320

(c)284

(d)324

S8. Ans.(b)

Sol. Average of first set = 376/8 =

47

Minimum number of second set = 47 + 15 =

62

47

Minimum number of second set = 47 + 15 =

62

Hence, required sum = 62 + 63 + 64 + 65 + 66 = 320

**Q9. Find the least number which, when**

divided by 72, 80 and 88, leaves the remainders 52, 60 and 68 respectively.

divided by 72, 80 and 88, leaves the remainders 52, 60 and 68 respectively.

(a) 7900

(b) 7800

(c) 7200

(d) 7600

S9. Ans.(a)

Sol. 72 – 52 = 20, 80 – 60 = 20, 88 – 68 = 20. We

see that in each

see that in each

case, the remainder is less than

the divisor by 20. The LCM

the divisor by 20. The LCM

of 72, 80 and 88 = 7920, therefore,

the required number 7920

the required number 7920

– 20 = 7900

**Q10. The HCF and LCM of two numbers**

are 44 and 264 respectively. If the first number is divided by 2, the quotient is

44. What is the other number?

are 44 and 264 respectively. If the first number is divided by 2, the quotient is

44. What is the other number?

(a) 108

(b) 44

(c) 124

(d) 132

S10. Ans.(d)

Sol. The first number = 2 × 44 = 88

The second number = (HCF* LCM)/88

= (44* 264)/88

= 132

**Q11. The product of two number is**

2160 and their HCF is 12. Find the possible pairs of numbers.

2160 and their HCF is 12. Find the possible pairs of numbers.

(a) 1

(b) 2

(c) 3

(d) 4

S11. Ans.(b)

Sol. HCF = 12. Then let the numbrs

be 12x and 12y.

be 12x and 12y.

Now 12x × 12y = 2160

xy = 15

Possible values of x and y are (1,

15); (3, 5); (5, 3); (15, 1)

15); (3, 5); (5, 3); (15, 1)

the possible pairs of numbers (12, 180) and

(36, 60)

(36, 60)

**Q12.Twice the square of a number is**

six times the other number. What is the ratio of the first number to the second?

six times the other number. What is the ratio of the first number to the second?

(a) 1: 4

(b) 2: 5

(c) 1: 3

(d) Cannot be determined

**Q13. If 19/5 is subtracted from 33/5 and difference is multiplied by 355 then what will be the final number?**

(a) 1004

(b) 884

(c) 774

(d) 994

**Q14. An army Commander wishing to draw up his 5180 men in the form of a solid square found that he had 4 men less. If he could get four more men and form the solid square, the**

**number of men in the front row is-**

(a) 72

(b) 68

(c) 78

(d) 82

**Q15. At the first stop on his route, a driver unloaded 2/5 of the packages in his van. After he unloaded another three packages at his next stop, 1/2 of the original number of packages remained. How many packages were in the van before the first delivery?**

(a) 25

(b) 10

(c) 30

(d) 36