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Quantitative Ability Tech Test Divisibility Test 3

2628.If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
0
1
2
None of these
Explanation:

Sum of digits = 5 + 1 + 7 + $ x $ + 3 + 2 + 4 = 22 + $ x $, which must be divisible by 3.

$\therefore$  $ x $ = 2.

2636.If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
2
5
6
7
Explanation:

Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.

$\therefore$   $ x $ = 7.

2643.On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
0
1
2
4
Explanation:

Let the number be $ x $ and on dividing $ x $ by 5, we get $ k $ as quotient and 3 as remainder.

$\therefore$    $ x $ = 5k + 3

$\Rightarrow$    $ x $2 = (5k + 3)2

   = (25 k 2 + 30$ k $ + 9)

   = 5(5 k 2 + 6$ k $ + 1) + 4

$\therefore$On dividing $ x $2 by 5, we get 4 as remainder.

2648.How many 3 digit numbers are divisible by 6 in all ?
149
150
151
166
Explanation:

Required numbers are 102, 108, 114, ... , 996

This is an A.P. in which $ a $ = 102, $ d $ = 6 and $ l $ = 996

Let the number of terms be $ n $. Then,

$ a $ + $\left( n - 1\right)$ d = 996

  $\Rightarrow$ 102 + $\left( n - 1\right)$ x 6 = 996

  $\Rightarrow$ 6 x $\left( n - 1\right)$ = 894

  $\Rightarrow$ $\left( n - 1\right)$ = 149

  $\Rightarrow$ $ n $ = 150.

2654.If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
2
5
6
None of these
Explanation:

Clearly, 4864 is divisible by 4.

So, 9P2 must be divisible by 3. So, 9 + P + 2 must be divisible by 3.

$\therefore$ P = 1.

2661.What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
4
3
2
1
Explanation:

6) 4456 (742

    42

    -------

     25

     24

    -------

      16

      12

    --------

       4

Therefore, Required number = (6 - 4) = 2.

2666.If the number 5 * 2 is divisible by 6, then * = ?
2
3
6
7
Explanation:

6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by $ x $.

Then, 5 + $x$ + 2 must be divisible by 3. So, $ x $ = 2.

2686.Which one of the following numbers is completely divisible by 45?
181560
331145
202860
2033555
Explanation:

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.

2687.Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?
11
16
25
30
Explanation:

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

     = 324 x 3 x 4 x 10

     = (324 x 4 x 30), which is divisible by30.

2689.The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
$ \dfrac{12}{35} $
$ \dfrac{1}{35} $
$ \dfrac{35}{8} $
$ \dfrac{7}{32} $
Explanation:

Let the numbers be $ a $ and $ b $. Then, $ a $ + $ b $ = 12 and ab = 35.

$\therefore \dfrac{a + b}{ab} $=$ \dfrac{12}{35} $      $\Rightarrow$  $ \left(\dfrac{1}{b} +\dfrac{1}{a} \right) $=$ \dfrac{12}{35} $

$\therefore$ Sum of reciprocals of given numbers =$ \dfrac{12}{35} $

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