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 numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Find the greatest number that will divide $400$, $435$ and $541$ leaving $9$, $10$ and $14$ as remainders respectively

  1. $17$
  2. $4$
  3. $55$
  4. $11$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$400-9=391$


$435-10=425$


$541-14=527$

$391=17\times23$

$425=5\times5\times17$

$527=17\times31$

 HCF of $391,425$ and $527=17$ 

Required number$=17$ 

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

A number when divided by  $156$  gives  $29$  as remainder. If the same number is divided by  $13$ , what will be the remainder?

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

Given number = 156x + 29
=156x + 26 + 3
= 13 $\displaystyle \times $ 12x + 13 $\displaystyle \times $ 2 + 3
= 13(12x + 2) + 3
$\displaystyle \therefore $  When the number is divided by 13 the remainder will be 3

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

LCM of the numbers $17$ and $5$ is 

  1. $105$
  2. $95$
  3. $85$
  4. $5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Factors are $ 17 = 1 \times 17$
$5 = 1 \times 5 $
$\therefore $ LCM of $17$ and $5$  $= 1 \times 17 \times 5 = 85$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

The greatest number with four digits which when divided by $3, 5, 7, 9$ leaves the remainders $1, 3, 5, 7$ respectively, is _______.

  1. $9763$
  2. $9673$
  3. $9367$
  4. $9969$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since on dividing by $3$ the remainder is $1$, the sum of digits of the number must add upto a number, dividing which by $3$ we get remainder $1$

Since on dividing by $5$ remainder is $3$, unit place digit has to be either $3$ or $8$
Since on dividing by $9$ remainder is $7$, sum of digits should give remainder $7$ when divided by $9$ 
Only options (A), (B) satisfy these criteria
Since (A) is bigger, we divide it by $7$ and find remainder which turns out to be $5$. 

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

When $31513$ ad $34369$ are divided by a certain three digit number, the remainders are equal, then the remainder is ______.

  1. $86$
  2. $97$
  3. $374$
  4. $113$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the divisor be $a$ and remainder be $r$

Let $31513 = am+r$
and $34369 = an+r$
Then, $a(n-m) = 2856 = 24\times119 = 12\times238 = 8\times357= 6\times476=4\times714$
All three digit numbers give same remainder $=$ $97$

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

The number of possible pairs of number, whose product is 5400 and the HCF is 30 is

  1. 1

  2. 2

  3. 3

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

$ Given\quad that\quad product\quad of\quad the\quad number\quad is\quad 5400=30\times 3\times 2\times 30.\ \therefore \quad Possible\quad pairs\quad as\quad per\quad the\quad requirment\quad are-\ (1)\quad 30\times (3\times 2\times 30)=30\times 180\ (2)\quad (30\times 3)\times (2\times 30)=90\times 60\ \therefore \quad Total\quad number\quad of\quad pairs=2\quad \quad (Ans) $

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

If HCF of numbers $408$ and $1032$ can be expressed in the form of $1032x -408 \times 5$, then find the value of $x$.

  1. $0$
  2. $1$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$408=2\times2\times2\times3\times17$

$1032=2\times2\times2\times3\times43$

Hence, $HCF=2\times2\times2\times3=24$

Now, $1032x-408\times5=24\Rightarrow 1032x=2064\Rightarrow x=2$

Multiple choice computer and ms office mathematical methods for economics economics

_________ is the largest number which when divides $100$ and $83$ leaves a remainder of $4$ and $3$ in each case.

  1. $14$
  2. $12$
  3. $16$
  4. $20$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We need the HCF of (100-4) and (83-3), which is the HCF of 96 and 80. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The greatest common factor is 16.

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

The product of two numbers is $2240$ and their HCF is $14$. Which of the following is not the possible pair.

  1. $(14,160)$
  2. $(28,80)$
  3. $(42, 80)$
  4. $(56,40)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pair in Option C is not possible.
because in option C pair is $(42,80)$
Since, Product of numbers $=42\times 80 =3360$
Option C is correct.