Arithmetic Reasoning problems
- 1. There are n boxes and m fruits. If we put 3 fruits in each box 3 fruits will be excess. If we put 4 fruits in each box 1 box will be excess. Find number of boxes and fruits ?
Options- A. 3 & 9
- B. 6 & 19
- C. 7 & 24
- D. 5 & 18 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 7 & 24
Explanation:
7 boxes & 24 Balls.
Let, n = No. of boxes ; m = No. of fruits
3n+3 = m---------->(1)
4(n-1)= m---------->(2)
=>4n-4 = 3n+3;
=>4n-3n = 4+3
n = 7
Put n=7 in eqn(1)
=> 3(7)+3 = m
21+3 = m
m = 24;
Number of boxes = 7 and fruits = 24
- 2. The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6 and 7, 7, 7, 7, 7, 7, 7 is ?
Options- A. 6
- B. 9
- C. 7
- D. 5 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 5
Explanation:
Arithmatic mean = sum/members
=> (1x1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7) / (1 + 2 + 3 + 4 + 5 + 6 + 7)
=> 140/28 = 5
- 3. Which statement best compares a line and a point?
Options- A. A point has no dimension and a line has one dimension.
- B. A line can have line segments on it whereas a point cannot be on any line segment.
- C. point is a location whereas a line has several planes located on it
- D. A line can lie on a plane whereas a point cannot lie on a plane. Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: A point has no dimension and a line has one dimension.
Explanation:
A point has no dimension and a line has one dimension is the statement that best compares a line and a point.
- 4. Every integer is a rational number.
Options- A. TRUE
- B. FALSE Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: TRUE
Explanation:
Yes, Every integer is a rational number. A rational number is a number which can be expressed as a ratio of two integers numerator and denominator where (the denominator not being 0 ).
Hence, Every integer can be expressed in ratio of two integers.
- 5. There are two examinations rooms P and Q. If 10 students are sent from P to Q, then the number of students in each room is the same. If 20 candidates are sent from Q to P, then the number of students in P is double the number of students in Q. The number of students in room Q is ?
Options- A. 100
- B. 70
- C. 120
- D. 80 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 80
Explanation:
If 'k' is number of students in P and 'l' is number of students in Q, then
From the given conditions, we have
=> k - 10 = l + 10 .......(1)
=> k + 20 = 2(l - 20) ....(2)
Solving these eqns, we get
k = 100 and l = 80.
Therefore, number of students in class Q is 80.
- 6. On sport?s day, if 12 children were made to stand in each column, 98 columns could be formed. After a certain music being played the plan was that the children have to stand in concentric circles such that the innermost circle will have one student, the next circle will have two students, the third circle will have 3 students and so on. How many circles will be formed in this manner ?
Options- A. 44
- B. 46
- C. 48
- D. 49 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 48
Explanation:
No. of students will be 98 x 12 = 1176
let us consider n circles then 1 + 2 + 3 + ....+ n = 1176
n(n+1)/2 = 1176
n = 48 circles.
- 7. Find by how much percentage the average of first 10 odd numbers (starting from 1) is greater than the last term ?
Options- A. 991/16 %
- B. 900/19 %
- C. 874/13 %
- D. 719/17 % Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 900/19 %
Explanation:
First ten odd numbers form an arithmetic progression of the form
1,3,5,7,9......
here a = first term = 1
d = common difference = 2
Average of first n numbers = (2a + (n - 1)d)/2
n th term of the AP = a + (n - 1)d
Substituting a = 1, d = 2 and n = 10 in the above formulas
average of first 10 numbers = 10
10 th term of the AP = 19
Therefore average of first 10 terms is 19 - 10 = 9 greater than
the last term. Hence the average is greater than the sum by
9/19 X 100 = 900/19 %
- 8. In a street, there are certain number of houses. People in that street are decided to paint their houses with certain colours. If four houses are painted with each colour, then one house will be left without any colour. If five houses are painted with each colour, then one colour will remain. Find the number of houses in that street ?
Options- A. 25
- B. 6
- C. 32
- D. 7 Also asked in: AIEEE, Bank Exams, CAT, Bank PO
Correct Answer: 25
Explanation:
Let x be number of houses and y be colors.
on the basis of question
x = 4y+1
x = 5(y-1)
on solving these 2 equations x = 25
- 9. There are five bags. In the first bag we put some fruits. Each bag the number of fruits is reduced by 1/4. The last bag contains 4. Then the number of fruits in the first bag is ?
Options- A. 2596
- B. 1024
- C. 256
- D. 64 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 1024
Explanation:
Fruits reduced by 1/4.
Total no. of bags N = 5
Formula to find no. of fruits in 1st bag = 4^n
Last Bag = 4 fruits.
That means, 4th bag = 4 x 4 = 16 fruits
3rd bag = 16 x 4 = 64 fruits
2nd bag = 64 x 4 = 256 fruits
1st bag = 256 x 4= 1024 fruits.
- 10. If in an A.P series 18th term is 29 and 29th term is 18. Then find the 49th term ?
Options- A. -3
- B. -2
- C. 0
- D. 1 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: -2
Explanation:
We know that in A.P series
18th term = a + 17d
29th term = a + 28d
But given
a + 17d = 29..........(i)
a + 28d = 18......... (ii)
Solving equation (i) and (ii), we get
d = -1
put d = -1 in any of the above equations and we get,
a = 46
Now, we know 49th term can be written as, a + 48d
putting the value of a and d in the above equation,
a + 48d = 46 + 48(-1)
= 46 - 48
= -2
Hence, the 49th term is -2.
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