APTITUDE I

Numbers

Example
1605 × 1605 = (1605)2
= (1600 + 5)2
= (1600)2 + 52 + 2 × 1600 × 5
= 2560000 + 25 16000
= 2576025

Exercise
1. The unit’s digit in the product (3127)173 is
a) 1 b) 3 c) 7 d) 9
Ans: c) 7
2. The difference between the place values of 7 in the numeral 574873 is
a) 69930 b) 59930 c) 96390 d) 69305
Ans: a) 69930
3. The unit’s digit in the product (274×318×577×313) is
a) 2 b) 3 c) 4 d) 5
Ans: a) 2
4. The digit in this unit place of the number represented by (795 – 358) is
a) 7 b) 0 c) 6 d) 4
Ans: d) 4
5. Given that (12 + 22 + 32 + … + 102) = 385, then the value of (22 + 42 + 62 + … + 202) is equal to
a) 770 b) 1540 c) 1155 d) (385)2
Ans: b) 1540
6. If x * y = (x + 2) 2. (y – 2), then the value of (7*5) is
a) 175 b) 205 c) 213 d) 243
Ans: d) 243
7. If 2x – 1 + 2x+1 = 320, then the value of x is
a) 4 b) 5 c) 6 d) 7
Ans: d) 78. If the number 42573 * is completely divisible by 72, then which of the following number should replace the asterisk ?
a) 4 b) 5 c) 6 d) 7
Ans: c) 6
9. There is one number which is formed by writing one digit 6 times (e.g. 111111, 444444 etc.). Such number is always divisible by
a) 7 b) 11 c) 13 d) All of these
Ans: d) All of these
10. The number nearest to 99547 which is exactly divisible by 687 is
a) 100166 b) 98928 c) 99479 d) 99615
Ans: d) 99615


H.C.F. & L.C.M. of Numbers

Example

A) H.C.F of 23 × 32 × 5 × 74, 22 × 35 × 52 × 73, 23 × 53 × 72 ?
Sol: The prime numbers common to given numbers are 2, 5 & 7.
H.C.F. = 22 × 5 × 72 = 980.
B) L.C.F of 22 × 33 × 5 × 72, 23 × 32 × 52 × 74, 2 × 3 × 53 × 7 × 11 ?
Sol: L.C.M. = product of highest powers of 2,3,5,7 and 11.
= 23 × 33 × 53 × 74 × 11.

Exercise

1. Two numbers are in the ratio of 15: 11. If their H.C.F. is 13, then the numbers are
a) 75, 55 b) 105, 77 c) 15, 11 d) 195, 143
Ans: d) 195,143.
2. The sum of two numbers is 528 and their H.C.F. is 33. The number of pair of such numbers satisfying and above condition is
a) 6 b) 12 c) 8 d) 4
Ans: d) 43. The L.C.M. of three different numbers is 120. Which of the following can not be their H.C.F.?
a) 8 b) 12 c) 24 d) 35
Ans: d) 35
4. The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is
a) 30 b) 36 c) 46 d) 56
Ans: c) 46
5. The least number of five digits which is exactly divisible by 12, 15 and 18 is
a) 10010 b) 10015 c) 10020 d) 10080
Ans: d) 10080
6. The largest number which divides 25, 73 and 97 to leave the same remainder in each case is
a) 24 b) 23 c) 21 d) 6
Ans: a) 24
7. What is the least number which when divided by 8,9,12 and 15 leaves the same remainder 1 in each case is
a) 179 b) 181 c) 359 d) 361
Ans: d) 361
8. What is the greatest number of three digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case is
a) 975 b) 996 c) 939 d) 903
Ans: a) 975
9. The H.C.F. and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is
a) 50 b) 100 c) 125 d) 250
Ans: c) 125
10. Six bells commence tolling together and toll at intervals of 2, 4, 6,8,10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
a) 4 b) 10 c) 15 d) 16
Ans: d) 16

Decimal Fractions

Example

67.32+? = 431.146
Sol: Let 67.32 + X = 431.146.
Then, X = (431.146 – 67.32) = 363.826.

Exercise

1. If 1.125 × 10k = o.oo1125, then the value of k is
a) -4 b) -3 c) -2 d) -1
Ans: b) -3
2.4.8438 /.069 =?
a) 60.2 b) 70.2 c) 69.2 d) 71.2
Ans: b) 70.2
3. The value of (3.75×3.75 –2×3.75×2.75+2.75+2.75×2.75) is
a) 1 b) 1.75 c) 4.75 d) 6.50
Ans: a) 1
4. The expression (11.98 × 11.98 + 11.98×X+.02×.02) will be a perfect square for x equal to
a) .02 b).2 c).04 d) 0.4
Ans: c) .04
5. The value of (25.732)2 – (15.732)2 is
a) 414.64 b) 41.464 c) 4146.4 d) 401464
Ans: a) 414.64
6. 0.7683 + 0.369 + 0.05 + 0.8 =?
a) 0.8065 b) 1.9873 c) 0.8110 d) None
Ans : b) 1.9873
7. 5463 +546.3 – 54.63 / ? = 5999.3
a) .05463 b) .5463 c) 5.463 d) None
Ans: c) 5.463
8. 852.2109 + 106.78 – 59.157 = ?
a) 899.8339 b) 889.8339 c) 899.9833 d) 804.5879
Ans: a) 899.8339
9. (.08 × .007) is equal to
a) .056 b) .0056 c).00056 d) .56
Ans: c).00056
10. 1 litre of water weighs 1 k.g. How many cubic milliletres of water with weighs 0.1 gm?
a) 0.1 b) 1 c) 10 d) 100
Ans: d) 100

Average

Example

There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Er 1. What was the original expenditure of the mess?
Sol. Let the original average expenditure be Rs X. Then,
42 (X – 1) – 35X = 42.
→ 7X = 84 → X = 12.
Original expenditure = Rs (35 × 12) = Rs 420.

Exercise

1. The average of first five prime numbers is
a) 4.5 b) 5 c) 5.6 d) 7.5
Ans: c) 5.6
2. The average of first five multiple of 3 is
a) 3 b) 9 c) 12 d) 15
Ans: b) 9
3. The average of four consecutive even numbers is 27. The largest of these numbers is
a) 36 b) 32 c) 30 d) 28
Ans: c) 30
4. The average of two numbers is M. if one number is N, then the other number is
a) 2 N b) 2 M c) M – N d) 2 M – N
Ans: d) 2 M – N
5. Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, the largest number is
a) 24 b) 36 c) 72 d) 108
Ans: c) 72
6. The average of ten numbers is 7. If each number is multiplied by 12, then the average of new set of numbers is
a) 7 b) 19 c) 82 d) 84
Ans: d) 84
7. The average of 11 observation is 60. If the average of first five observations is 58 and that of the last five is 56, then the sixth observation is
a) 90 b) 110 c) 85 d) 100
Ans: d) 100
8. In seven given numbers, the average of first four numbers is 4 and that of the last four numbers is also 4. If the average of these seven numbers is 3, the fourth number is
a) 3 b) 4 c) 7 d) 11
Ans: b) 4
9. The average age of 30 students is 9 years. If the age of their teacher is included, it becomes 10 years. The age of the teacher (in years) is
a) 27 b) 31 c) 35 d) 40
Ans: d) 40
10. The average weight of 9 mangoes increases by 20 g if one of them weighing 120 g is replaced by another. The weight of the new mango is
a) 180 g b) 200 g c)260 g d) 300 g
Ans: d) 300 g