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Problems on Numbers Questions

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A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3D?


A13

B3

C42

DCannot be determined

Answer: Option B

Explanation:

Let's number is N
so N = DX + 8 -------(1)
N = 3DY + 21 ---------(2)

From Eq. 1 & 2
=> D(X-3Y) = 13
"13" is prime number, and its factors will be 1 and 13 only
=> X-3Y must be 1
Let X = 4 and Y = 1, D=13
So, N = 60
Remainder Left = 2N / 3D
= 120 / 39 = 3

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The shopkeeper charged 12 rupees for a bunch of chocolate. but i bargained to shopkeeper and got two extra ones, and that made them cost one rupee for dozen less then first asking price. How many chocolates I received in 12 rupees ?


A10

B16

C14

D18

Answer: Option B

Explanation:

n chocolates = Rs 12
Price per dozen = 144/n
I got n+2 in rs 12 = > Price per dozen = 144/n+2
144/n+2 = 144/n - 1
=> n = 16

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The sum of the four consecutive two digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can be one of these four numbers?


A31

B25

C41

D67

Answer: Option C

Explanation:

Let the numbers are 2a +1, 2a + 3, 2a + 5, 2a + 7 and their sum = 8a + 16
Given that if this sum is divided by 10, results in a perfect square.
So, (8a+16)/10 = k^2.
=> a = (10k^2?16) /8
=> a=[ 5(k^2)/4 ]?2
As k^2 is a perfect square and has to be divided by 4, only even numbers should be considered for k.
For k = 2, we get, a = 3, but 2a + 1 is not a two digit number.
For k = 4, a = 18 for which the given condition is satisfying.
So the numbers are 37, 39, 41, 43.
For k = 6, a = 43. The number are 87, 89, 91, 93.

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What is the greatest power of 143 which can divide exactly 125!


A12

B11

C8

D9

Answer: Option D

Explanation:

Here is no explanation for this answer

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Smallest no which when multiplied by 12748 gives a perfect square is


A3187

B3183

C3245

D4532

Answer: Option A

Explanation:

Here is no explanation for this answer

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The least number that must be subtracted from 63520
to make the result a perfect square, is:


A16

B20

C24

D30

Answer: Option A

Explanation:

Here is no explanation for this answer

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In this problem, ABS(x) provides absolute value of x, without regard to its sign. For example ABS(3) = ABS(-3) = 3
The graphs of y = – ABS(x – a) + b and y = – ABS(x – c) + d intersect at points (2,5) and (8, 3).
Find a + c


A8

B10

C7

D5

Answer: Option A

Explanation:

Both curves intersect at (2, 5)
So 5 = – |2 – a| + b ? 5 + |2 – a| – b = 0 - - - (1)
5 = – |2 – c| + d ? 5 + |2 – c| – d = 0 - - - (2)
Also,
3 = – |8 – a| + b ? 3 + |8 – a| – b = 0 - - - (4)
3 = – |8 – c| + d ? 3 + |8 – c| – d = 0- - - (4)
Equating 1 and 3, 5 + |2 – a| = 3 + |8 – a| ? 2 + |2 – a| = |8– a|
So a = 4
Similarly if we equate 2 and 4, we get c = 4
a + c = 8

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For a scholarship, n out of 2n + 1 students are to be selected. If the number of different ways in which at least one student can be selected is 63, then the maximum number of students to be selected are :


A3

B4

C2.5

D5

Answer: Option C

Explanation:

Here is no explanation for this answer

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Given n = 1 + x and x is a product of four consecutive integers. Then which of the following is true ?
A. n is an odd integer B. n is prime C. n is a perfect square


Aboth A and C are correct

Bboth A and B are correct

Conly A is correct

Donly C is correct

Answer: Option A

Explanation:

Take any 4 values, like 2, 3, 4, 5 and get the answer a & c only.

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How many of the numbers x (x being integer) with 10 <= x <= 99 are 18 more than the sum of their digits


A9

B12

C18

D10

Answer: Option D

Explanation:

Let the number be ab. So given that
=>10a + b = 18 + a + b
=> 9a = 18
=> a = 2
So 20, 21, ... upto 29 there are total 10 numbers possible.

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