## Number System Questions and Answers Part-3

1. A two digit number ab is added to another number ba, which is obtained by reversing the digits then we get three digit number. Thus (a + b) equals to:
a) at least 18
b) 2ab
c) 2(a + b)
d) (a + b) ≥ 10

Explanation: When two 2 digit numbers are added and the resultant value is a three digit number. It means there must be a carry over (i.e. The sum of unit digits be greater than 9. Similarly, the sum of the tens digit is also greater than 9)
Required numbers = 64 + 46 = 110
So, Option 'd' is correct.

2. A gardener plants his garden with 5550 trees and arranged them so that there is one plant more per row as there are rows then number of trees in a row is:
a) 56
b) 74
c) 76
d) 75

Explanation: Let there be n rows, then number of trees in each row = (n + 1)
Total number of trees,
n × (n +1) = 5550
Now, at this moment this problem can be solved in two ways. First by finding the roots of quadratic equation. Second, by using the values from options.
74 × 75 = 5550
i.e. (n + 1) = 75

3. The sum of two numbers is 18. The greatest product of these two number can be:
a) 17
b) 80
c) 81
d) Can't determined

Explanation: a + b = 18
Maximum of (a × b) will be only when a = b
Thus, a = b = 9
Maximum of (a × b) = 9 × 9 = 81.

4. The unit digit of (316)34n + 1 is :
a) 4
b) 5
c) 1
d) 7

Explanation: The unit digit of (316)34n, depends on the power of 6.
See the pattern, 62 = 36
63 = 216
64 = 1296
Any power of 6 will give unit digit 6.
The unit digit of (316)34n always 6.
So, unit digit of (316)34n + 1 will be 7

5. A number when divided by 14 leaves reminder of 8, but when the same number is divided by 7, it will leave the remainder :
a) 3
b) 2
c) 1
d) 4

Explanation: When the number is divided by 14 it gives a remainder of 8,
The number = 14N + 8 (14N is divisible by 14)
When same number is divided by 7 it will give remainder 1

6. The HCF and LCM of 24, 82, 162, 203 are :
a) 23, 32000
b) 24, 32000
c) 24, 25600
d) 22, 3200

Explanation: HCF of 24, 82, 162, 203 = 24
LCM of 24, 82, 162, 203 = 24 = 28 × 125 = 32000

7. The four digit smallest positive number which when divided by 4, 5, 6 or 7, it leaves always the remainder as 3:
a) 1000
b) 1257
c) 1263
d) 1683

Explanation: The least possible number = (LCM of 4, 5, 6 and 7) + 3
= 420 + 3
= 423
The next higher number is,
(420m + 3), now we put a least value of m such that
(420m + 3) ≥ 1000
At m = 3,
value = 420 × 3 + 3 = 1263

8. A string of length 221 metre is cut into two parts such that one part is $$\frac{9}{4}$$ th as long as the rest of the string, then the difference between the larger piece and the shorter piece is
a) 58 m
b) 53 m
c) 85 m
d) 76 m

Explanation: Let one part of string is x.
x + $$\frac{{9{\text{x}}}}{4}$$ = 221 m
x = 68 meter
and, $$\frac{{9{\text{x}}}}{4}$$ = 153 m
Difference between two parts = 153 - 68 = 85 m

9. The sum of 100 terms of the series 1 - 3 + 5 - 7 + 9 - 11 .......... is:
a) 100
b) -200
c) 200
d) -100

10. The remainder of $$\frac{{{6^{36}}}}{{215}}:$$
\eqalign{ & \frac{{ {{6^{36}}} }}{{215}},\,{\text{can}}\,{\text{be}}\,{\text{written}}\,{\text{as}} \cr & \frac{{{{\left( {{6^3}} \right)}^{12}}}}{{215}} \cr & \frac{{{{216}^{12}}}}{{215}},\,[216\,{\text{on}}\,{\text{divided}}\,{\text{by}}\,215,\,{\text{gives}}\,{\text{remainder}}\,1] \cr & \frac{{{1^{12}}}}{{215}} \cr & {\text{The}}\,{\text{remainder}}\,{\text{will}}\,{\text{be}}\,1 \cr}