Quant Quiz "Number system" for SSC CGL 2016

Q1. A five digit number is made using digits 2, 8, 4, 7 and 6. Is the number divisible by 9?
(a) Yes
(b) No
(c) Can’t say
(d) None of these

1. Ans.(a)
Sol.
We know that divisibility of 9 is the sum of all the digits divisible by 9
Sum of digit = 2 + 8 + 4 + 7 + 6 = 27
Which is divisible by 9
So the digit formed by these five number always be divisible by 9.

Q3. The LCM of two numbers is 1680 and their HCF is 120. If one number is 504, find the other number.
(a) 204
(b) 320
(c) 400
(d) 560

3. Ans.(c)
Sol.
Let the other number = x
LCM × HCF = first number × second number
1680 × 120 = 504×x
x=(1680 ×120)/504=400

Q4. Consider the following statements related to three numbers i.e. 24984, 26784 and 28584 are
I. They are divisible by 3
II. They are divisible by 4
III. They are divisible by 9.
Which of these are correct?
(a) All 3
(b) Only I and II
(c) Only II and III
(d) Only I and III

4. Ans.(a)
Sol.
Sum of these number is 27, 27 and 27 respectively.
All three numbers divisible by 9 since 27 is divisibly by 9.
If number is divisible by 9 it will also divisible by 3.
Last two digits of these number is 84, which is divisible by 4. So number is also divisible by 4.
Hence all three are correct.

Q5. The HCF and LCM of two numbers are 12 and 72 respectively. If the sum of two numbers is 60, then one of the two numbers will be
(a) 12
(b) 24
(c) 50
(d) 72

5. Ans.(b)
Sol.
Let the first number = x
Second number = y
x×y= LCF × HCF
xy = 12 × 72 = 864
x + y = 60
x = 24
y = 36

Q6. If two numbers are in the ratio 6 :13 and their least common multiple is 312, then what is the sum of numbers?
(a) 57
(b) 67
(c) 75
(d) 76

6. Ans.(d)
Sol.
Let the first number = 6x
Second number = 13x
LCM of first and second number = 6 × 13 × x
6 × 13x = 312
x=312/(6×13)
x = 4
Sum of number = 6 × 4 + 13 × 4 = 76

Q7. When n is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4?
(a) 1
(b) 3
(c) 2
(d) None of these

7. Ans.(c)
Sol.
n = 4x + 3
2n = 2(4x + 3)
2n = 8x + 6
According to question,
Remainder =(8x + 6)/4
remainder = 2

Q8. Find the smallest number required to be added to 2000 to get a number exactly divisible by 17.
(a) 6
(b) 4
(c) 2
(d) 3

8. Ans.(a)
Sol.
When 2000 is divided by 17 remainder is equals to 11
Smallest number required to be added = 17 – 11 = 6

Q9. Two numbers are in the ratio 3: 4, and their LCM is 108. Find their HCF.
(a) 9
(b) 8
(c) 6
(d) 5

9. Ans.(a)
Sol.
Let the first number = 3x
Second number = 4x
LCM of these two number = 3 × 4x = 12x
12x = 108
x = 9
HCF of these two number = x
= 9

Q10. A number P4571203K is divisible by 18. Which of the following values can P and K take?
(a) 1, 2
(b) 2, 3
(c) 3, 3
(d) 6, 8

10. Ans.(d)
Sol.
Number = P4571203K
If the number is divisible by 18, then it should be divisible by 2 and 9
So, P + 4 + 5 + 7 + 1 + 2 + 0 + 3 + k = 22 + P + K
⇒ P + K = 5 or P + K = 14
And K must be even number or zero
So, from the following option (d) option fulfilled the condition.

Q11. Find the least number which when divided by 12, 15, 20 and 35 leaves a remainder 6 in each case?
(a) 216
(b) 426
(c) 846
(d) None of these

11. Ans.(b)
Sol.
LCM (12, 15, 20, 35) = 420
Number, which leaves a remainder 6 in each case = 420 + 6 = 426

Q14. Four bells ring together. If the bells ring at intervals of 2, 5, 8 and 10 second respectively, after what interval of time will they ring together again?
(a) 40 second
(b) 25 second
(c) 30 second
(d) 35 second

14. Ans.(a)
Sol.
Time after which bells ring together = LCM (2, 5, 8, 10) second = 40 second

Q15. What is the LCM of these three numbers 3/4,5/6 &7/8?

(a) 105/2

(b) 108/4

(d) None of these

15. Ans.(a)

Sol.

LCM of fraction =(LCM of Numerator)/(HCF of Denominator)

=(LCM (3,5,7))/(HCF (4,6,8) )

=105/2