Q 1. Answer: D
Explanation:
91 is divisible by 7. So, it is not a prime number.
Q 2. Answer: A
Explanation:
91 is divisible by 7. So, it is not a prime number.
1397 x 1397 = (1397)^2
= (1400 - 3)^2
= (1400)^2 + (3)^2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Q 4. Answer: A
Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3 x = 11.
Third integer = x + 4 = 15
Q 5. Answer: B
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4
Explanation:
91 is divisible by 7. So, it is not a prime number.
Q 2. Answer: A
23)
1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
Explanation:
91 is divisible by 7. So, it is not a prime number.
1397 x 1397 = (1397)^2
= (1400 - 3)^2
= (1400)^2 + (3)^2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Q 4. Answer: A
Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3 x = 11.
Third integer = x + 4 = 15
Q 5. Answer: B
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4
Q 6. Answer: B
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8
Q 7. Answer: A
Required number = H.C.F. of (91 – 43 = 48), (183 – 91 = 92) and (183 – 43 = 140)
= H.C.F. of 48, 92 and 140 = 4
Q 8. Answer: D
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together (30/2) + 1 = 16 times.
Q 9. Answer: C
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600
Q 10. Answer: C
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Required number = H.C.F. of (91 – 43 = 48), (183 – 91 = 92) and (183 – 43 = 140)
= H.C.F. of 48, 92 and 140 = 4
Q 8. Answer: D
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together (30/2) + 1 = 16 times.
Q 9. Answer: C
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600
Q 10. Answer: C
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.