Question 1
The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.
A
1500✓✗
B
1600✓✗
C
1550✓✗
D
None of these✓✗
Explanation
Difference of squares = (sum) × (difference) = 75 × 20 = 1500
(Using the identity a2 - b2 = (a + b)(a - b))
Question 2
A number consists of two digits. The digit in the tens place is 3 times the digit in the unit's place. If 54 is subtracted, the digits are reversed. The number is:
A
39✓✗
B
92✓✗
C
93✓✗
D
94✓✗
Explanation
Let the units digit = u, so the tens digit = 3u.
Number = 30u + u = 31u. Reversed number = 10u + 3u = 13u.
31u - 54 = 13u
18u = 54
u = 3
Number = 31 × 3 = 93
Question 3
In a two-digit number, the digit in the ten's place is twice the digit in the unit's place. If 18 is subtracted from the number, the digits are reversed. Find the number.
A
63✓✗
B
21✓✗
C
42✓✗
D
None of these✓✗
Explanation
Let the unit's digit = u, so the ten's digit = 2u.
Number = 20u + u = 21u. Reversed number = 10u + 2u = 12u.
21u - 18 = 12u
9u = 18
u = 2
Number = 21 × 2 = 42
Question 4
The sum of two numbers is 62 and their product is 960. The sum of their reciprocals is
A
31480✓✗
B
29480✓✗
C
61960✓✗
D
41960✓✗
Explanation
Sum of reciprocals = 1a + 1b = a + bab = 62960 = 31480
Question 5
A number consists of two digits. The digit in the ten's place is 3 times the digit in the unit's place. If 54 is subtracted from the number, then the digits are reversed. The number is:
A
39✓✗
B
62✓✗
C
93✓✗
D
31✓✗
Explanation
Let the unit's digit = u, so the ten's digit = 3u.
Number = 30u + u = 31u. Reversed number = 10u + 3u = 13u.
31u - 54 = 13u
18u = 54
u = 3
Number = 31 × 3 = 93
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