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Numbers
All the numbers from 1,2,3,4 ......... are natural numbers, N and all the
numbers from 0,1,2,3,.... are whole numbers, W . The number divisible
only by 1 and itself is called prime numbers. The lowest prime number and
only even prime number is 2. The lowest odd prime number is 3.
Divisibility test
• Divisibility by 2: A number is divisible by 2, if its last digits is 0 or
divisible by 2.
• Divisibility by 3: A number is divisible by 3, if the sum of the digits is
divisible by 3.
• Divisibility by 4: A number is divisible by 4, if the last two digits are
divisible by 4.
• Divisibility by 5: A number is divisible by 5, if its last digits is 0 or 5.
• Divisibility by 6: A number is divisible by 6, if it is divisible by 2 and 3.
• Divisibility by 7: A number is divisible by 7, if the last digit is doubled
and subtracted from the number by other digits. The resultant number
must be divisible by 7.
• Divisibility by 8: A number is divisible by 8, if the last three digits are
divisible by 8.
• Divisibility by 9: A number is divisible by 9, if the sum of the digits is
divisible by 9.
• Divisibility by 10: A number is divisible by 10, if the last digit is 0.
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Quick Quantitative Aptitude
• Divisibility by 11: A number is divisible by 11, if the difference of the
sum of the digit in odd places and that in even places is either zero or
divisible by 11.
• Divisibility by 12: A number is divisible by 12, if the number is divisible
by 4 and 3.
Order of arithmetic operations
Order of arithmetic operations are Bracket, Division, Multiplication, Addition and Subtraction from left to right.
Exercises
1. How many prime numbers less than 42 are there?
(a) 12
(b) 15
(c) 11
(d) 13
2. Find the numbers whose factors are (i) the largest 2 digit prime number
and (ii) smallest 3 digit prime number.
(a) 1111
(b) 9797
(c) 8548
(d) 5981
3. The number of times 86 is subtracted from 3876 so that the remainder
is less than 86 is
(a) 6
(b) 4
(c) 8
(d) 7
4. Find the least positive number which when decreased by 13 times is
equal to 36 times the reciprocal of the number.
(a) 3
(b) 12
(c) 4
(d) 7
5. Find the number, when 10 is added from 6 times the number, the result
is 100 more thrice the number.
(a) 30
(b) 40
(c) 50
(d) 60
6. Find the unit’s digit in 484302 + 484303 .
(a) 1
(b) 0
(c) 2
(d) 3
Numbers
3
7. x × 0.05 × 0.0025 = 0.000625. Find x.
(a) 0.05
(b) 5
(c) 0.5
(d) 0.005
8. The product of three consecutive multiples of 6 is divisible by
(a) 2040
(b) 1984
(c) 2548
(d) 1296
(c) 40
(d) 20
9. 320 + 321 + 322 + 323 is divisible by
(a) 30
(b) 22
10. If a positive number is multiplied by 17 and 19 is added to the product
and if the resulting number is divisible by 19, then the least original
number is
(a) 19
(b) 17
(c) 11
(d) 15
11. What is the product of all prime numbers between 80 and 90?
(a) 8249
(b) 5841
(c) 6482
(d) 7387
12. What is the difference between the place value of 2 in the numeral
4567?
(a) 0
(b) 440
(c) 11
(d) 30
13. If 32165 x 4 is divisible by 4, then the digit in place of x is
(a) 1
(b) 3
(c) 0
(d) 7
14. If each of three non zero numbers a,b,c is divisible by 5, then abc must
be divisible by
(a) 125
(b) 140
(c) 110
(d) 130
(b) 100
(c) 50
(d) 20
15. 10 × 63 ÷ 7 + 10
(a) 9
Key
1)
7)
13)
d
b
c
2)
8)
14)
b
d
a
3)
9)
15)
a
c
b
4)
10)
c
a
5)
11)
a
d
6)
12)
b
b
4
Quick Quantitative Aptitude
Solution
1. (d)
Prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41. 13 numbers are
there.
2. (b)
Largest 2 digit prime number = 97
Smallest 3 digit prime number = 101
Their product is 9797
3. (a)
4. (c)
Let the number be x
36
x
x2 − 13x − 36 = 0
(x − 4)(x − 9) = 0
x − 13 =
x = 4, 9
5. (a)
6x + 10 = 3x + 100
3x = 90
x = 30
6. (b)
484302 + 484303
42 gives unit digit 6 and 43 gives unit digit 4.
Numbers
4302 gives unit digit 6.
4303 gives unit digit 4.
unit digit in 484302 + 484303 = unit’s digit is (6 + 4) = 0
7. (b)
x × 0.05 × 0.0025 = 0.000625
0.000625
=5
x=
0.05 × 0.0025
8. (d)
The first three multiples of 6 are 6,12,18
= 63 (1 + 2 + 3)
Product is divisible by 63 × 6 = 1296.
9. (c)
320 + 321 + 322 + 323 = 320 (1 + 3 + 32 + 33 )
= 320 (40)
320 × 40 is divisible by 40
10. (a)
Let x be the least number.
17x + 19
Original number =
19
Since both 17,19 prime, x should be 19.
11. (d)
Prime numbers between 80 and 90 are 83 and 89.
Product of 83 × 89 = 7387
12. (b)
500 − 60 = 440
13. (c)
From given choices, consider last two digits and divide it by 4.
(a) 3216514 is not divisible by 4.
5
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Quick Quantitative Aptitude
(b) 3216534 is not divisible by 4.
(c) 3216504 is divisible by 4, since the last two digit is divisible by4.
(d) 3216574 is not divisible by 4.
14. (a)
Sine each one the numbers a,b,c is divisible by 5, the number represented as 5a, 5b, 5c. Product of three numbers is 5a × 5b × 5c =
125(abc).
15. (b)
10 × 63 ÷ 7 + 10 = 10 × (63 ÷ 7) + 10
63
+ 10
= 10 ×
7
= 90 + 10
= 100