Quantitative Aptitude

Number System

616 Questions
All HCF and LCM Word Problems 416 Remainder Theorems 122 Number Properties and Series 21 Successive Division 20 Divisibility Rules 19 Digit Word Problems 9 Decimal and Fraction Operations 6 Unit Digit and Last Digits 2 BODMAS Simplification 1

Number System Questions

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find the greatest number which divides 120, 165 and 210 exactly leaving remainders 5, 4 and 3 respectively

  1. 7

  2. 5

  3. 23

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The required number will be the H.C.F of (120 - 5), (165 - 4) and (210 - 3) i.e. H.C.F. of 115
161 and 207
$\displaystyle \therefore $ Required number = H.C.F. of 115, 161 and 207 = 23

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Greatest number which divided $926$ and $2313$, leaving $2$ and $3$ remainders, respectively, is?

  1. $462$
  2. $54$
  3. $152$
  4. $154$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A number divides 926 and 2313 leaving remainders 2 and 3 respectively.

This means that the number perfectly divides 926 - 2 = 924 as well as 2313 - 3 = 2310.

Now we simply need to find the HCF of 924 and 2310 

On calculating the HCF , we get it as  462

Hence, the answer is 462

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The greatest integer that divides 358, 376, 334 leaving the same remainder in each case is

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The difference between each set of two numbers is respectively 18, 42 and 24.
Now, as the remainder should be the same in each case, the number is the greatest common divisor of 18, 24 and 42.
$18=2\times 3\times 3$
$24=2\times 2\times 2\times 3$
$42=2\times 3\times 7$
$\therefore HCF=2\times 3=6$
$\therefore$ The required number is 6.

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

A number when divided by $14$ leaves a remainder of $8$, but when the same number is divided by $7$, it will leave the remainder ?

  1. 3

  2. 2

  3. 1

  4. can't be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We have,

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 $1.$

hence, this is the answer.

Multiple choice maths remainder and factor theorems linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

When a number is divided by $13$, the remainder is $11$. When the same number is divided by $17$, the remainder is $9$. What is the number ?

  1. $853$
  2. $278$
  3. $349$
  4. $670$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$x = 13p + 11$ and $x = 17q + 9$
$\therefore$ $13p + 11 = 17q + 9$
$\therefore$ $17q - 13p = 2$
$\therefore$ q $=\dfrac{2 + 13p}{17}$
The least value of p for which q $=\dfrac{2 + 13p}{17}$ is a whole number is $p = 26$
x $= (13 \times 26 + 11)$
$= (338 + 11)$
$= 349$

Multiple choice maths remainder and factor theorems linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

On dividing a number by $56$, we get $29$ as remainder. On dividing the same number by $8$, what will be the remainder ?

  1. $4$
  2. $5$
  3. $6$
  4. $7$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Applying remainder theorem i.e. $A=bq+r $
where, $b$ = divisior 
$r$ = remainder 
$\therefore A = 56q + 29$
if q = 1 
The no. is $A = 85$
On dividing by $8$, Remainder $(r) =5$

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

What number should be subtracted from each of the numbers 54, 71, 75 and 99, so that the remainders may be in proportion?

  1. 5

  2. 4

  3. 3

  4. 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number to be subtracted is $x$

$(54-x),  (71-x),   (75-x)$  and $ (99-x)$ are in proportion

$\Rightarrow \dfrac{54-x}{71-x}=\dfrac{75-x}{94-x}$ Which is true if $x=3$


$\Rightarrow \dfrac{54-3}{71-3}=\dfrac{75-3}{94-3}$

$\Rightarrow \dfrac{51}{68}=\dfrac{72}{91}$

i.e $\Rightarrow \dfrac{3}{4}=\dfrac{3}{4}$

Then subtracted $3$ in these number may be in proportion  

Multiple choice

There is a set of positive integers called Number Box which contains positive integers which when divided by 2, 3, 4, 5, 6 leave the remainders of 1, 2, 3, 4, 5 respectively. What is the maximum value of square root of the number of numbers that can be in the Number Box such that it does not contain any number with 4 digits?

  1. 4

  2. 8

  3. 5

  4. 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number N satisfies N = LCM(2,3,4,5,6) * k - 1 = 60k - 1. We need 60k - 1 < 1000. 60k < 1001, k < 16.68. There are 16 such numbers (k=1 to 16). The square root of 16 is 4.

Multiple choice

If we divide a two-digit number by a number consisting of the same digits written in the reverse order, we get 1 as a quotient and 18 as a remainder. If we add 33 in the given number, we get the sum of the squares of the digits constituting that number. Find the number.

  1. 63

  2. 79

  3. 91

  4. 97
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the number be 10x + y. The condition (10x + y) / (10y + x) = 1 remainder 18 implies (10x + y) = (10y + x) + 18, which simplifies to 9x - 9y = 18 or x - y = 2. Checking 97: 9 - 7 = 2, and 97 / 79 = 1 remainder 18. Also, 97 + 33 = 130, and 9^2 + 7^2 = 81 + 49 = 130.