Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.
16. 2 + 22 + 23 + … + 29 =?
A.2044
B.1022
C.1056
D.None of these
Answer
Explanation:
This is a G.P. in which a = 2, r = 22/2 = 2 and n = 9.
Sn = a(rn – 1)/ (r – 1) = 2 x (29 – 1)/ (2 – 1) = 2 x (512 – 1) = 2 x 511 = 1022.
17. How many terms are there in the G.P. 3, 6, 12, 24, … , 384 ?
A.8
B.9
C.10
D.11
E.7
Answer
Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, tn = 384=arn-1 = 384
3 x 2n – 1 = 384
2n-1 = 128 = 27
n – 1 = 7
n = 8
Number of terms = 8.
18. What is the smallest 6 digit number exactly divisible by 111?
A. 100010
B. 100011
C. 100012
D. 100013
Answer
Explanation:
Smallest 6 digit number = 100000
100000/111 = 900, remainder = 100. Hence 11 more should be added to 100000 to get the smallest 6 digit number exactly divisible by 111
Smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011
19. If the number 653 xy is divisible by 90, then (x + y) = ?
A.2
B.3
C.4
D.6
Answer
Explanation:
90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653×0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.
20. How many 3 digit numbers are completely divisible 6 ?
A. 146
B. 148
C. 150
D. 152
Answer
Explanation:
100/6 = 16, remainder = 4. Hence 2 more should be added to 100 to get the minimum 3 digit number divisible by 6.
Minimum 3 digit number divisible by 6 = 100 + 2 = 102
999/6 = 166, remainder = 3. Hence 3 should be decreased from 999 to get the maximum 3 digit number divisible by 6.
Maximum 3 digit number divisible by 6 = 999 – 3 = 996
Hence, the 3 digit numbers divisible by 6 are 102, 108, 114,… 996
This is Arithmetic Progression with a = 102 ,d = 6, l=996
Number of terms =(l−A.d+1=(996−102)6+1=8946+1=149+1=150
20. The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?
A.12/35
B.1/35
C.35/8
D.7/32
Answer
Explanation:
Let the numbers be a and b. Then, a + b = 12 and ab = 35.
(a + B)/ab = 12/35 1/b + 1/a = 12/35
Sum of reciprocals of given numbers = 12/35
21. If n is a natural number, then (6n2 + 6n) is always divisible by:
A. Both 6 and 12
B. 6 only
C. 12 only
D. None of these
Answer
Explanation:
6n2 + 6n = 6n(n + 1)
Hence 6n2 + 6n is always divisible by 6 and 12 (∵ remember that n (n + 1) is always even)
22. The difference between the place values of two sevens in the numeral 69758472 is
A.0
B.6993
C.699930
D. None of these
Answer
Explanation:
Required difference = (700000 – 70) = 699930
23. Which of the following number is divisible by 24?
A. 31214
B. 61212
C. 512216
D. 3125832
Answer
Explanation:
If a number is divisible by two co-prime numbers, then the number is divisible by their product also. If a number is divisible by more than two pairwise co-prime numbers, then the number is divisible by their product also.
If a number is divisible by another number, then it is also divisible by all the factors of that number. 24 = 3 × 8 where 3 and 8 are co-prime numbers.
3 and 8 are also factors of 24. Hence if a number is divisible by 3, and 8, the number will be divisible by their product 24 also.
If a number is not divisible by 3 or 8, it is not divisible by 24
31214 is not divisible by 3 and 8 = 31214 is not divisible 24
61212 is not divisible by 8 though it is divisible by 3 = 61212 is not divisible 24
512216 is not divisible by 3 though it is divisible by 8 =512216 is not divisible 24
3125832 is divisible by 3 and 8 = 3125832 is divisible 24
24. Which of the following numbers will completely divide (461 + 462 + 463 + 464)?
A.3
B.10
C.11
D.13
Answer
Explanation:
(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10.
25. What is the largest 4 digit number exactly divisible by 88?
A. 9944
B. 9999
C. 9988
D. 9900
Answer
Explanation:
Largest 4 digit number = 9999
9999 ÷ 88 = 113, remainder = 55
Hence largest 4 digit number exactly divisible by 88 = 9999 – 55 = 9944
26. What will be remainder when 17200 is divided by 18?
A.17
B.16
C.1
D.2
Answer
Explanation:
When n is even. (xn – an) is completely divisibly by (x + A.
(17200 – 1200) is completely divisible by (17 + 1), i.e., 18.
(17200 – 1) is completely divisible by 18.
On dividing 17200 by 18, we get 1 as remainder.
27. If 60% of 3/5 of a number is 36, then the number is:
A.80
B.100
C.75
D.90
Answer
Explanation:
Let the number be x. Then
60% of 3/5 of x = 36
60/100 x 3/5 x x = 36
x = 36 x 25/9 = 100
Required number = 100
28. Find the number of factors of 60.
A. 6
B. 10
C. 12
D. 15
Answer
Explanation:
60 = (2^2) *(3^1) * (5^1)
Hence, the no. of factors =3*2*2 = 12
29. Which one of the following is a prime number?
A.161
B.221
C.373
D.437
E.None of these
Answer
Explanation:
437 > 22
All prime numbers less than 22 are: 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, and 221 is divisible by 13.
373 is not divisible by any of the above prime numbers.
373 is prime.
30. A 3-digit number 4a3 is added to another 3-digit number 984 to give the four digit number 13b7, which is divisible by 11. Then, (a + b) is :
A. 10
B.12
C.11
D.15
Answer
Explanation:
a + 8 = b ⇒ b – a = 8.
Also 13b7 is divisible by 11, so (7 + 3) – (b + 1) = 0 or b = 9.
Now, b – a = 8 and b = 9. So, a = 1. a + b = (1 + 9) = 10.
