Mathematics - Playing with Numbers
Exam Duration: 45 Mins Total Questions : 20
The number (10n - 1) is divisible by 11 for
- (a)
n \(\epsilon \) N
- (b)
Odd values of n
- (c)
Even values of n
- (d)
n is the multiple of 11
The values of A and 8 in the given addition respectively are __
2 3 A
+A 3 B
- (a)
4, 7
- (b)
7, 4
- (c)
5, 6
- (d)
6, 5
The greatest value that must be given to x so that the number 7713 x 8 is divisible by 4 is __________
- (a)
1
- (b)
6
- (c)
8
- (d)
7
If 1 A where A and 8 are single digit numbers, such that 8 - A = 3, then the values of A and 8 respectively are _________
x A
_____
B 6
______
- (a)
4, 5
- (b)
9, 6
- (c)
5, 4
- (d)
6, 9
Suppose that the division N + 5 leaves a remainder of 4 and the division N + 2 leaves a remainder of 1. What must be the ones digit of N?
- (a)
7
- (b)
3
- (c)
9
- (d)
4
Given that the number 148101a095 is divisible by 11, where a IS single digit number, what are the possible values of a?
- (a)
4
- (b)
1
- (c)
7
- (d)
9
The largest natural number by which the product of three consecutive even natural numbers IS always divisible, is ______
- (a)
16
- (b)
24
- (c)
48
- (d)
96
If in a number, difference between the sum of digits at its odd places and that of digits at the even places is given 0, then the number is divisible by _______
- (a)
7
- (b)
9
- (c)
5
- (d)
11
A 5-digit number xy235 is divisible by 3 such that x + y < 5, where x and y are single digits, then possible values of (x, y) are ________
- (a)
(1,1)or(4,0)
- (b)
(1,1) or (2,0)
- (c)
(1,1) or (0,2)
- (d)
(2, 0) or (0, 2)
If 1 A B and there is no carry on addition then the value of 8 is ________
C C A
______
6 9 7
______
- (a)
5
- (b)
4
- (c)
3
- (d)
2
If N divided by 5 leaves a remainder of 3, then one's digit of N must be ________
- (a)
Either 3 or 6
- (b)
Either 3 or 8
- (c)
Either 8 or 1
- (d)
Either 8 or 6
Given that the number 67y19 is divisible by 9, where y is a single digit, what is the least possible value of y?
- (a)
3
- (b)
9
- (c)
7
- (d)
4
A 3-digit number 'eba' is divisible by 3 if ________
- (a)
a + 2b + e is divisible by 3
- (b)
2a + b + e is divisible by 3
- (c)
a + b + 2e is divisible by 3
- (d)
a + b + e is divisible by 3
If A B, then the value of B is _________
x A 3
_____
5 7 B
_____
- (a)
5
- (b)
2
- (c)
0
- (d)
4
In a division, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 48, then dividend is ___________
- (a)
240
- (b)
576
- (c)
4800
- (d)
4848
Which of the following statements is INCORRECT?
- (a)
All even natural numbers which are divisible by 3 are also divisible by 6.
- (b)
If a natural number is divisible by 21, then it is divisible by both 3 and 7.
- (c)
If AB x 4 = 192, then A + B = 10
- (d)
A number of the form 14 N + 2 leaves the remainder 2 when divided by 7
Fill in the blanks
(i) If sum of 3-digit numbers xyz, yzx and zxy is divided by (x + y + z), then quotient is ___P__.
(ii) The difference between 2-digit numbers ab and ba, (where a > b) is divided by 3. The quotient is ___Q___.
(iii) Sum of a 2-digit number and the number obtained by reversing its digits is always divisible by ____R____
- (a)
P Q R 111 3(a + b) 11 - (b)
P Q R 99 (a + b) 7 - (c)
P Q R 111 3(a - b) 11 - (d)
P Q R 99 (a - b) 3
Match the following.
Column-I | Column-II |
---|---|
(P) If 213x27 is divisible by 9, then x = | (i) 2 |
(Q) If 2415x is divisible by 6 then x = | (ii) 8 |
(R) If 23245x is divisible by 4 and 3, then x = | (iii) 3 |
(S) If 7251x93 is divisible by 11, then x = | (iv) 6 |
- (a)
(P) \(\rightarrow\) (iii); (Q) \(\rightarrow\)(ii); (R) \(\rightarrow\) (iv); (S) \(\rightarrow\) (i)
- (b)
(P) \(\rightarrow\) (ii); (Q) \(\rightarrow\) (iv); (R) \(\rightarrow\) (i); (S) \(\rightarrow\) (iii)
- (c)
(P) \(\rightarrow\) (iii); (Q) \(\rightarrow\) (iv); (R) \(\rightarrow\) (i); (S) \(\rightarrow\) (ii)
- (d)
(P) \(\rightarrow\) (ii); (Q) \(\rightarrow\) (iii); (R) \(\rightarrow\) (i); (S) \(\rightarrow\) (iv)
How many 5-digit numbers of the form AABAA is divisible by 33?
- (a)
1
- (b)
3
- (c)
0
- (d)
infinite
Find the value of A, Band C respectively
(i) A 8 3
x C 9
________
A 0 4 A
+1 5 B B 0
____________
C C A 0 A
___________
(ii) 4 3 A 4
x 3 A
________________
B 7 C 7 6
+ B C 0 C 2 0
_________________
B 4 7 6 9 6
__________________
- (a)
(i) 2 6 7 (ii) 9 5 2 - (b)
(i) 6 7 2 (ii) 4 3 1 - (c)
(ii) 7 5 2 (ii) 9 2 5 - (d)
(i) 7 6 2 (ii) 4 1 3