Q1) If the sum two numbers is 31 and their product is 240, then find the absolute difference between the numbers.
A. 1
B. 3
C. 4
D. 5
E. None of these
Explanation
Correct Option: (A)
Let two numbers be x and y
We are given that, sum of two numbers x + y = 31 and product = xy = 240
Therefore,
x – y = (x + y)2 – 4xy
Substituting the values, we get
x – y = (31)2 – 4 × y
= 961 – 960
= 1
= 1
The required difference between the numbers is 1.
Q2) The sum of squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find their sum.
A. 35
B. 42
C. 20
D.18
E. None of these
Explanation
Correct Option: (c)
Let the three numbers be x, y and z.
Given: Sum of squares of three numbers is 138 and sum of their products taken two at a time is 131
Therefore,
x2+y2+z2=138
xy+yz+zx=131
Formula: (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
This formula can be used to easily find the sum of three numbers. Substituting the values, we get
(x + y + z) 2 = x2 + y2 + z2 + 2 (xy + yz + zx)
(x + y + z ) 2 = 138 + 2(131)
(x + y + z ) 2 = 400
Hence, (x + y + z) = 20
Q3) The average of 3 consecutive even numbers is 18, find the largest of these numbers.
A. 15
B. 16
C. 20
D. 26
E. None of these
Explanation
Correct Option: (c)
Let the numbers be x, x +2, and x + 4
Hence, sum of these numbers = (average x no. of numbers) = (18 x 3) = 54
x + (x +2) + (x + 4) = 54
3x = 48
x = 16
Largest number = (x + 4) = (16 + 4) = 20
Q4) . 5 times a positive number is less than its square by 24. What is the integer?
A. 5
B. 8
C. 7.5
D. 9
E. None of these
Explanation
Correct Option: (B)
Let the unknown number be x.
5 times a positive number = 5x
5 times a positive number is less than its square by 24
x2 – 5x = 24
x2 + 3x – 8x – 24
x (x + 3) – 8(x + 3)
(x – 8) (x + 3)
x = 8
8 is the required integer.
Q5) The sum of numerator and denominator of a fraction is 30. If 2 is added to numerator and 2 is subtracted from denominator, then it becomes 2/3. Find the fraction.
A. 1/2
B. 1/3
C. 2/3
D. 1/4
E. None of these
Explanation
Correct Option: (A)
Read the question breaking stepwise and understand given parameters.
1) Let the fraction be a
b
2) Sum of numerator and denominator=a+b=30—–(1)
3) 2 is added to numerator and 2 is subtracted from denominator. Hence,
a + 2 = 2
b – 2 3
3(a+2)=2(b-2)
Solving, we get
3a+6=2b-4
3a-2b=-10—–(2)
Solve equations (1) and (2), we get
a = 10 and b = 20
Therefore, the fraction = 10/20 = 1/2
