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ARITHMETIC

ARTHMETIC  INTERVIEW QUESTION AND ANSWERS

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

  1. 897
  2. 164,850
  3. 164,749
  4. 149,700
  5. 156,720

The correct choice is (B)

Explanation:

The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.

The next number that will leave a remainder of 2 when divided by 3 is 104, 107, .... 

The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.

So, the given series is an AP with the first term being 101 and the last term being 998 and thhe common difference being 3.

Sum of an AP =   


We know that in an A.P., the nth term an = a1 + (n - 1) X d

In this case, therefore, 998 = 101 + (n - 1) X 3

i.e., 897 = (n - 1) X 3

Therefore, n - 1 = 299 

Or n = 300.

Sum of the AP will therefore, be   = 164,850

 If the total distance of a journey is 120 km .If one goes by 60 kmph and comes back at 40kmph what is the average speed during the journey? 

A . 30 mph

B.  45 mph

C.  48 mph

D.  40mph

Ans: 48kmph


A school has 30% students from Maharashtra .Out of these 20% are Bombey students. Find the total percentage of Bombay?


A.  8%

B.  5%

C.  1%

D.  6%

Ans: 6%

How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?

  1. 128
  2. 142
  3. 143
  4. 141
  5. 129

The correct choice is (5)

Explanation

The smallest 3-digit positive integer that when divided by 7 leaves a remainder of 5 is 103.
The largest 3-digit positive integer that when divided by 7 leaves a remainder of 5 is 999.

The series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an A.P (arithmetic progression) with the first term being 103 and the last term being 999 having a common difference of 7.

We know that in an A.P, 'l' the last term is given by l = a + (n - 1) X d, where 'a' is the first term, 'n' is the number of terms of the series and 'd' is the common difference.

Therefore, 999 = 103 + (n - 1) X 7

Or 999 - 103 = (n - 1) X 7
Or 896 = (n - 1) X 7
Or n - 1 = 128
Or n = 129

An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it?

A. 9

B. 8

C. 2

D.  5

 Ans: 9

If A/B = 3/5,then 15A = ?


A.  6B

B. 9B

C. 7B

d. 8B

 Ans : 9B


The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with m+2?

  1. m + 4
  2. n + 6
  3. n + 3
  4. m + 5
  5. n + 4

The correct choice is (5).

Explanation:

The fastest way to solve problems of this kind is to take numerical examples.

The average of 5 consecutive integers from 1 to 5 is 3. Therefore, the value of m is 1 and the value of n is 3.

Now, the average of 9 consecutive integers starting from m + 2 will be average of integers from 3 to 11.

The average of numbers from 3 to 11 is 7.

Now look at the answer choices. Only choice (E) satisfies this condition.

 Each side of a rectangle is increased by 100% .By what percentage does the area increase?

 A. 200%

B. 100%

C.  300%

D.  400%

Ans : 300%

Perimeter of the back wheel = 9 feet, front wheel = 7 feet on a certain distance, the front wheel gets 10 revolutions more than the back wheel .What is the distance?

A. 215 feet

 B.  300 feet

C. 310 feet

D. 315 feet

Ans : 315 feet.

If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?

  1. 3
  2. 1/3
  3. 2
  4. 9
  5. 1/9

The correct choice is (3) and

Explanation

The sum of the first n terms of a G.P. is given by  , where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P.

Therefore, the sum of the first 6 terms of the G.P will be equal to 

And sum of the first 3 terms of the G.P. will be equal to   

The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1 

i.e.   

=>   

=> r3 + 1 = 9 

=> r3 = 8 

=> r = 2

Perimeter of front wheel =30, back wheel = 20. If front wheel revolves 240 times. How many revolutions will the back wheel take?

A. 320 times

B. 315 times

C. 360 times

D. 250 times

Ans: 360 times


20% of a 6 litre solution and 60% of 4 litre solution are mixed. What percentage of the mixture of solution


A. 35 %

B. 36%

C. 32 %

D. 30%

 Ans: 36%


City A's population is 68000, decreasing at a rate of 80 people per year. City B having population 42000 is increasing at a rate of 120 people per year. In how many years both the cities will have same population?


A. 120 years

B. 150 years

C. 140 years

D.  135 years

Ans: 130 years

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

  1. 300
  2. 120
  3. 150
  4. 170
  5. 270

The correct choice is (C)

Explanation:

The sum of the 4th and 12th term = 20.

Let t1 be the first term, t4 be the fourth term, and t12 be the 12th term

Then t4 + t12 = 20

t4 can be expressed as t1 + 3d
Similarly, t12 can be expressed as t1 + 11d

Then t4 + t12 = 20 can be expressed as   t1 + 3d + t1 + 11d = 20

=>      2t1 + 14d = 20 
=>      t1 + 7d =10
=>      t8 = 10

The sum of the first 15 terms = 
In an arithmetic progression t1 + t15 = t1 + t1 + 14d = 2t1 + 14d = 2(t1 + 7d) = 2(t8).
Therefore, the sum of the first 15 terms =  = 150 

Two cars are 15 kms apart. One is turning at a speed of 50kmph and the other at 40kmph . How much time will it take for the two cars to meet?

A. 3/2 hours

B. 1/2 hours

C. 2/3 hours

D. 4/3 hours

 Ans: 3/2 hours

13. Which of the following fractions is less than 1/3


(a) 22/62 
(b) 15/46
(c) 2/3
(d) 1

Ans: (b)

Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and that of set A?

  1. 2500
  2. 5050
  3. 11325
  4. 6275
  5. 2550

The correct choice is (1)

Explanation:

SET 1 - (2, 4, 6, 8,...., 50). A total of 25 consecutive even numbers.

SET 2 - (102, 104, 106,....., 150). Another set of 25 consecutive even numbers.

Difference between 1st term of set 1 and set 2 is 100. Difference between 2nd term of set 1 and set 2 is 100 and so on.

So total difference is (100 + 100 + 100 + ....) = 25 x 100 = 2500.

 Directions for questions 1-3: The questions are based on the information given below

Miss Dean wants to rennovate her house. She hires a plumber, a carpenter, a painter, an electrician and an interior decorator. The work to be finished in one working (Monday - Friday ). 


Each worker will take the full day to do his job. Miss Dean permits only one person to work each day.
I. The painter can work only after the plumber and the carpenter have finished their jobs
II. The interior decorator must do his job before the electrician.
III. The carpenter cannot work on Monday or Tuesday

1. If the painter work on Thursday, which one of the following alternatives is possible?


(a) The electrician works on Tuesday.
(b). The electrician works on Friday.
(c) The interior decorator works after the painter does.
(d). The painter works on consecutive days.
(e). Miss Dean cannot fit all of the workers int schedule
Ans: (b)


2. If the painter works on Friday which of the following must be false?

(a) . The carpenter may works on Wednesday
(b). The carpenter and the electrician may work on consecutive days
(c). If the carpenter works on Thursday, the electrician has to work on Wednesday
(d). The plumber may work before the electrician does
(e). The electrician may work on Tuesday
Ans: (c)


3. Which argument is possible?
(a). The electrician will works on Tuesday and the interior decorator on Friday
(b). The painter will work on Wednesday and plumber on Thursday
(c). The carpenter will works on Tuesday and the painter on Friday
(d). The painter will work on Monday and the carpenter on Thursday
(e). The carpenter will work on Wednesday and the plumber on Thursday
Ans: (e)

 

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