# Online Aptitude Test - Aptitude Test - Random

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**20**. - Time allotted:
**30**minutes. - Each question carries 1 mark; there are no negative marks.
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#### Marks : 2/20

##### Test Review : View answers and explanation for this test.

^{1793}x (625)

^{317}x (341

^{491})}?

Unit digit in (6374)^{1793} = Unit digit in (4)^{1793}

= Unit digit in [(4^{2})^{896} x 4]

= Unit digit in (6 x 4) = 4

Unit digit in (625)^{317} = Unit digit in (5)^{317} = 5

Unit digit in (341)^{491} = Unit digit in (1)^{491} = 1

Required digit = Unit digit in (4 x 5 x 1) = 0.

L.C.M. of 8, 16, 40 and 80 = 80.

7 | = | 70 | ; | 13 | = | 65 | ; | 31 | = | 62 |

8 | 80 | 16 | 80 | 40 | 80 |

Since, | 70 | > | 65 | > | 63 | > | 62 | , so | 7 | > | 13 | > | 63 | > | 31 |

80 | 80 | 80 | 80 | 8 | 16 | 80 | 40 |

So, | 7 | is the largest. |

8 |

Let the capacity of 1 bucket = *x*.

Then, the capacity of tank = 25*x*.

New capacity of bucket = | 2 | x |

5 |

Required number of buckets = | 25x |

(2x/5) |

= | 25x |
x | 5 | |

2x |

= | 125 |

2 |

= 62.5

Required run rate = | 282 - (3.2 x 10) | = | 250 | = 6.25 | ||

40 | 40 |

Video Explanation: https://youtu.be/GhK9d8tcqvA

Let the number be *x*.

Then, x + 17 = |
60 |

x |

*x*^{2} + 17*x* - 60 = 0

(*x* + 20)(*x* - 3) = 0

*x* = 3.

Increase in 10 years = (262500 - 175000) = 87500.

Increase% = | 87500 | x 100 | % = 50%. | |

175000 |

Required average = | 50 | % = 5%. | |

10 |

Let the required weight be *x* kg.

*Less weight, Less cost (Direct Proportion)*

250 : 200 **::** 60 : *x* 250 x *x* = (200 x 60)

x= |
(200 x 60) |

250 |

*x* = 48.

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes *x* days to do the work.

5 : 4 :: 20 : x x = |
4 x 20 | ||

5 |

*x* = 16 days.

Hence, Tanya takes 16 days to complete the work.

Formula: If A can do a piece of work in n days, then A's 1 day's work = |
1 | . |

n |

(A + B + C)'s 1 day's work = | 1 | + | 1 | + | 1 | = | 7 | . | ||

24 | 6 | 12 | 24 |

Formula: If A's 1 day's work = |
1 | , | then A can finish the work in n days. |

n |

So, all the three together will complete the job in | 24 | days | = | 3 | 3 | days. | |

7 | 7 |

Whole work is done by A in | 20 x | 5 | = 25 days. | ||

4 |

Now, | 1 - | 4 | i.e., | 1 | work is done by A and B in 3 days. | ||

5 | 5 |

Whole work will be done by A and B in (3 x 5) = 15 days.

A's 1 day's work = | 1 | , (A + B)'s 1 day's work = | 1 | . |

25 | 15 |

B's 1 day's work = | 1 | - | 1 | = | 4 | = | 2 | . | ||

15 | 25 | 150 | 75 |

So, B alone would do the work in | 75 | = 37 | 1 | days. |

2 | 2 |

Suppose they meet *x* hours after 7 a.m.

Distance covered by A in *x* hours = 20*x* km.

Distance covered by B in (*x* - 1) hours = 25(*x* - 1) km.

20*x* + 25(*x* - 1) = 110

45*x* = 135

*x* = 3.

So, they meet at 10 a.m.

Principal = Rs. | 100 x 5400 | = Rs. 15000. | ||

12 x 3 |

_{10}5 + log

_{10}(5

*x*+ 1) = log

_{10}(

*x*+ 5) + 1, then

*x*is equal to:

log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + 1

log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + log_{10} 10

log_{10} [5 (5*x* + 1)] = log_{10} [10(*x* + 5)]

5(5*x* + 1) = 10(*x* + 5)

5*x* + 1 = 2*x* + 10

3*x* = 9

*x* = 3.

If log_{x} |
9 | = - | 1 | , then x is equal to: |
||

16 | 2 |

log_{x} |
9 | = - | 1 | ||

16 | 2 |

x^{-1/2} |
= | 9 |

16 |

1 | = | 9 | |

x |
16 |

x = |
16 |

9 |

x = |
16 | 2 | ||

9 |

x = |
256 |

81 |

Let the side of the square(ABCD) be *x* metres.

Then, AB + BC = 2*x* metres.

AC = 2*x* = (1.41*x*) m.

Saving on 2*x* metres = (0.59*x*) m.

Saving % = | 0.59x |
x 100 | % | = 30% (approx.) | |

2x |

Volume of water displaced | = (3 x 2 x 0.01) m^{3} |

= 0.06 m^{3}. |

Mass of man | = Volume of water displaced x Density of water |

= (0.06 x 1000) kg | |

= 60 kg. |

A : B = 100 : 80.

A : C = 100 : 72.

B | = | B | x | A | = | 80 | x | 100 | = | 10 | = | 100 | = 100 : 90. | |||||

C | A | C | 100 | 72 | 9 | 90 |

B can give C 10 points.

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

Video Explanation: https://youtu.be/WCEF3iW3H2c

*Direction (Q.No. 19)*

Each of the numbers except 14 is an odd number.

The number '14' is the only EVEN number.

*Direction (Q.No. 20)*

Numbers are (2^{3} - 1), (3^{3} - 1), (4^{3} - 1), (5^{3} - 1), (6^{3} - 1), (7^{3} - 1) etc.

So, the next number is (8^{3} - 1) = (512 - 1) = 511.