Arithmetic Aptitude 4
Question 1 |
How many numbers between 20 and 451 are divisible by 9?
44 | |
48 | |
50 | |
52 |
Discuss it
Question 1 Explanation:
The required numbers are 27, 36, 45……450. This is an A.P. with a = 27 and d = 9 Let it has n terms. Then Tn = 450 = 27 + (n-1) x9 ∴ 450 = 27+ 9n - 9 ∴ 9n = 432 ∴ n = 48
Question 2 |
How many terms are there in 3,9,27,81........531441?
25 | |
12 | |
13 | |
14 |
Discuss it
Question 2 Explanation:
3, 9, 27, 81..............531441 form a G.P. with a = 3 and r = 9/3 = 3 Let the number of terms be nAccording to the formula, Nth term of the G.P is represented as Tn = a x rn-1
Then 3 x 3n-1 = 531441 ∴ 3n = 312 ∴ n = 12
Question 3 |
7 + 72 + 73...........76 =?
140136 | |
142156 | |
133256 | |
137256 |
Discuss it
Question 3 Explanation:
Given series is a G. P. with a = 7, r = 7 and n = 6 ∴ Sn = a(rn-1) / (r-1) ∴ Sn = 7(76-1) / 6 Sn = = 137256
Question 4 |
Two numbers are in the ratio of 2:9. If their H. C. F. is 19, numbers are:
6, 27 | |
8, 36 | |
38, 171 | |
20, 90 |
Discuss it
Question 4 Explanation:
Let the numbers be 2X and 9X Then their H.C.F. is X, so X = 19 ∴ Numbers are (2x19 and 9x19) i.e. 38 and 171
Question 5 |
Subhash has 90 currency notes, some of which are Rs. 1000 denomination and rest of Rs. 500 denomination. The total amount is Rs 71,000. How many notes he has in denomination of Rs. 500?
30 | |
32 | |
34 | |
38 |
Discuss it
Question 5 Explanation:
Let the no. of Rs. 500 note be X Then the no. of Rs. 1000 note = 90 – X ∴ 500X + 1000(90 – X) = 71000 ∴ 500X + 90000 – 1000X = 71000 ∴ 500X = 19000 ∴ X = 38
Question 6 |
If the average of four consecutive odd numbers is 12, find the smallest of these numbers?
5 | |
7 | |
9 | |
11 |
Discuss it
Question 6 Explanation:
Let the numbers be x, x+2, x+4 and x+6 Then (x + x + 2 + x + 4 + x + 6)/4 = 12 ∴ 4x + 12 = 48 ∴ x = 9
Question 7 |
If the sum of two numbers is 13 and the sum of their square is 85. Find the numbers?
6 & 7 | |
5 & 8 | |
4 & 9 | |
3 & 10 |
Discuss it
Question 7 Explanation:
Let the numbers be x and 13-x
Then x2 + (13 – x)2 = 85
∴ x2 + 169 + x2 – 26x = 85
∴ 2 x2 – 26x + 84 = 0
∴ x2 – 13x + 42 = 0
∴ (x-6)(x-7)=0
Hence numbers are 6 & 7
There are 7 questions to complete.