Number Theory - SSC

Find the smallest number which should be added to the smallest number divisible by 6, 9 and 15 to make it a perfect square.

• A.

  10

• B.

  9

• C.

  19

• D.

  21

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Find the sum of the greatest and the smallest number which may replace k in the number 3281k6 to make the number divisible by 6

• A.

  9

• B.

  8

• C.

  5

• D.

  4

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If 5x - $\frac{1}{4x}$ = 6, x > 0, then find the value of 25x² - $\frac{1}{16x^2}$

• A.

  $6\sqrt{41}$

• B.

  36

• C.

  $\sqrt{246}$

• D.

  $6\sqrt{31}$

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Three positive numbers are in the ratio 2 : 3 : 4. The sum of their squares is 2349. The average of the first two numbers is:

• A.

  36

• B.

  27.5

• C.

  18

• D.

  22.5

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Which of the following numbers is NOT divisible by 15?

• A.

  2595

• B.

  3195

• C.

  3465

• D.

  2995

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The mean proportional between a number and 20 is 50. What is that number?

• A.

  125

• B.

  8

• C.

  100

• D.

  $10\sqrt{10}$

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Which of the following numbers is NOT divisible by 150?

• A.

  320550

• B.

  333300

• C.

  463750

• D.

  201300

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The product of three consecutive odd numbers is 693. What is the smallest of the three numbers?

• A.

  9

• B.

  11

• C.

  5

• D.

  7

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How many positive two-digit numbers can be divided by 6?

• A.

  12

• B.

  15

• C.

  14

• D.

  13

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If the 9-digit number 5p42978n6 is divisible by 72, what is the value of (2p - 1), where n is the second largest of all the possible values of n? Given that p and n are natural numbers.

• A.

  17

• B.

  21

• C.

  15

• D.

  11

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The largest six-digit number exactly divisible by 81 is:

• A.

  999989

• B.

  999991

• C.

  999945

• D.

  999876

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How many numbers between 100 and 1000 are divisible by 17?

• A.

  51

• B.

  53

• C.

  52

• D.

  54

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 From the following numbers, find the number which exactly divisible by 42

• A.

  25232

• B.

  25242

• C.

  25244

• D.

  25212

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What is the remainder when 8127 is divided by 8?

• A.

  7

• B.

  5

• C.

  4

• D.

  6

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The sum of two numbers is 17 and their product is 34.Find the sum of their squares.

• A.

  224

• B.

  221

• C.

  225

• D.

  222

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When two numbers are separately divided by 44, the remainders are 11 and 38, respectively. If the sum of the two numbers is divided by 44, then the remainder will be:

• A.

  16

• B.

  44

• C.

  33

• D.

  5

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If the formula for converting degrees Fahrenheit to degrees Celsius is C = $\frac{5}{9}$(F - 32), what is the value of F when C is 30?

• A.

  86

• B.

  $-\frac{10}{9}$

• C.

  $-\frac{9}{10}$

• D.

  54

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Which of the following numbers is divisible by 33?

• A.

  178750

• B.

  164461

• C.

  185592

• D.

  171116

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Find the greatest among the following options.

• A.

  0.62

• B.

  $\frac{2}{3}$

• C.

  0.57

• D.

  $\frac{4}{5}$

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How many two-digit numbers are divisible by 3 or 5?

• A.

  48

• B.

  41

• C.

  42

• D.

  40

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What will be the smallest natural number to be filled in the blank for the number
’23_45678’ to be divisible by 22?

• A.

  7

• B.

  1

• C.

  9

• D.

  3

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If the sum of two numbers is 25 and their product is 144, then what is the position difference between the two numbers?

• A.

  8

• B.

  7

• C.

  16

• D.

  9

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What is the least square number which is exactly divisible by 2, 3 10, 18 and 20?

• A.

  196

• B.

  180

• C.

  30

• D.

  900

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Find the value of k in the number 3426k if the number is divisible by 6 but NOT divisible by 5.

• A.

  4

• B.

  6

• C.

  9

• D.

  3

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If each of the two numbers $5^{16}$ and $5^{25}$ are divided by 6, the remainders are $R_1$ and $R_2$, respectively. What is the value of $\frac{R_1+R_2}{R_2}$?

• A.

  $\frac{6}{5}$

• B.

  $\frac{1}{5}$

• C.

  $\frac{5}{6}$

• D.

  $\frac{1}{6}$

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