Hello Aspirants. Welcome to Online Quantitative Aptitude Section with explanation in AffairsCloud.com. Here we are creating question sample in **Number System**, which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

**What will be the Unit digit of 27!**

A.0

B.1

C.3

D.4

E.None of these

###### Answer & Explanation

Answer –**A.0**

**Explanation :**

1*2*3*………………………………26*27

Factorial after 6 should end with 0

**x**^{p}× x^{q}× x^{r}= 1 then p^{3}+q^{3}+r^{3}is equal to

A.0

B.1

C.pqr

D.3pqr

E.None of these

###### Answer & Explanation

Answer –**D.3pqr**

**Explanation :**

x^{p}× x^{q}× x^{r}= 1

x^{p+q+r }= 1

x^{ 0}= 1 => p+q+r = 1

p^{3}+q^{3}+r^{3}– 3pqr = (p+q+r)(p2+q2+r2-pq-qr-rp)

p^{3}+q^{3}+r^{3}– 3pqr = 0

p^{3}+q^{3}+r^{3}= 3pqr

**If the divisor is five times the quotient and six times the remainder, if the remainder is 5 then the dividend is**

A.225

B.300

C.185

D.412

E.None of these

###### Answer & Explanation

Answer –**C.185**

**Explanation :**

Q=6, R = 5

Dividend = divisor*Q + R

Dividend = 30*6 + 5 = 180+5 = 185

**If the sum and the product of 2 numbers are 25 and 144 respectively then the difference of the number should be**

A.11

B.9

C.7

D.15

E.None of these

###### Answer & Explanation

Answer –**C.7**

**Explanation :**

A+B = 25

AB = 24

(a-b)^{2}= (a+b)^{2}– 4ab

(a-b)^{2}= 25^{2}– 4(144)

(a-b)^{2}= 625 – 576

(a-b)^{2}= 49

a-b = 7

**The sum of the two digit number is 11. The number obtained by reversing the digit is 27 less than the original number.Then the original number is**

A.74

B.47

C.65

D.83

E.None of these

###### Answer & Explanation

Answer –**A.74**

**Explanation :**

4+7 = 11

74-47 = 27

**The product of 2 consecutive even number is 1224, then one of the number is**

A.26

B.36

C.28

D.42

E.None of these

###### Answer & Explanation

Answer –**B.36**

**Explanation :**

34*36 = 1224

**21**^{2}+22^{2}+23^{2}+…………………30^{2}= ?

A.5640

B.9455

C.6585

D.2870

E.None of these

###### Answer & Explanation

Answer –**C.6585**

**Explanation :**

1^{2}+2^{2}+3^{2}+…………………n^{2}= 1/6[n(n+1)(2n+1)]

= 30*31*61/6 – 20*21*41/6

= 9455 – 2870 = 6585

**A number when divided by 361 gives a remainder 47. If the Same number is divided by 19 ,the remainder is**

A.18

B.11

C.9

D.13

E.None of these

###### Answer & Explanation

Answer –**C.9**

**Explanation :**

47÷19=> remainder 9

Ex : 769 ÷ 361 => remainder 47

769 ÷ 19 => remainder 9

**The respective ratio between the two digit of a number is 5:3, if the digit at the one’s place is twice the digit at ten’s place.What is the number ?**

A.63

B.21

C.12

D.Can’t be determined

E.None of these

###### Answer & Explanation

Answer –**D.Can’t be determined**

**Explanation :**

2x/x = 5/3

6x = 5x

**N is the smallest number which when added to the 2000 makes the resulting number divisible by 12, 16, 18 and 21, Then the N is**

A.11

B.7

C.9

D.16

E.None of these

###### Answer & Explanation

Answer –**D.16**

**Explanation :**

LCM of 12, 16, 18, 21 = 1008

1008*2 = 2016

N = 16

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