Numbers Questions

Q:

What should be the maximum value of B in the following equation?
8A9 – 6B2 + 4C6 = 723

 A) 4 B) 1 C) 5 D) 7

Explanation:

1 1
8 A 9
+ 4 C 6
-  6 B 2
7 2 3
We may represent the given sum, as shown below:

1 + A + C - B = 12
A + C - B = 11

Now,giving the maximum values to A and C, i.e.

A = 9 and C = 9, we get B = 7.

4 69
Q:

How many prime numbers exist in $\inline \fn_jvn \small \fn_jvn \small 6^{5}\times 35^{9}\times 11^{3}$ ?

 A) 29 B) 31 C) 33 D) 27

Explanation:

Given  $\inline&space;6^{5}\times&space;35^{9}\times11&space;^{3}$

$\inline&space;\Rightarrow&space;\left&space;(&space;2\times&space;3\right&space;)^{5}&space;\times&space;\left&space;(&space;5\times&space;7\right&space;)^{9}&space;\times11^{3}$ $\inline&space;\small&space;\Rightarrow2&space;^{5}\times&space;3^{5}\times&space;5^{9}\times&space;7^{9}\times11&space;^{3}$

Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

Filed Under: Numbers - Quantitative Aptitude - Arithmetic Ability
Exam Prep: CAT
Job Role: Bank PO

4 66
Q:

How many remainders are possible if $\inline \fn_jvn \small \left (16 \right )^{n}$ is divided by 9 for any positive integral value of n ?

 A) 1 B) 2 C) 3 D) 4

Explanation:

When $\inline&space;\fn_jvn&space;\small&space;(16)^{n}$ is divided by 9, we have

$\inline \fn_jvn \small \frac{16^{1}}{9}$, remainder = 7

$\inline \fn_jvn \small \frac{16^{2}}{9}$, remainder = 4

$\inline \fn_jvn \small \frac{16^{3}}{9}$, remainder = -8 or 1

$\inline \fn_jvn \small \frac{16^{4}}{9}$, remainder = 7

$\inline \fn_jvn \small \frac{16^{5}}{9}$, remainder = 4

$\inline \fn_jvn \small \frac{16^{6}}{9}$, remainder = 1.

So, we have cyclicity of 3 factors i.e 7,4,1.

Hence only 3 remainders are possible.

5 58
Q:

Find the next number in the series 125, 80, 45, 20, ....

 A) 5 B) 15 C) -5 D) 10

Explanation:

The pattern is -45, -35, -25, -15

The next number = 20-15= 5

7 45
Q:

Find the next number in the series 141,137,146,130,155,119,...

 A) 147 B) 168 C) 162 D) 182