1. Value of p is

Question

Paragraph for Questions: There are two sets A and B each of which consists of three numbers in AP whose sum is 15 and where D and d are the common differences such that D - d = 1. If p/q= 7/8 where p and q are the product of the numbers, respectively, and d > 0, in the two sets, then

1.  Value of p is

(A) 100

(B) 120

(C) 105

(D)  110

2.  Value of q is

(A)  100

(B)  120

(C)  105

(D)  110

3.  Value of D + d is

(A)  1 

(B)  2

(C)  3 

(D)  4

Answer 1

Correct answer 1. (C)  2. (B) 3. (C)

1. Let the numbers in set A be a - D, a, a + D and in set B be b - d, b, b + d

3a = 3b = 15

⇒ a = b = 5

Set A = {5 - D, 5, 5 + D}

Set B = {5 - d, 5, 5 + d}

where D = d + 1

25(8 - 7) = 8 (d + 1)2 - 7d2

⇒ d = - 17, 1 but d > 0

⇒ d = 1

So, numbers in set A are 3, 5, 7 and numbers in set B are 4, 5, 6.

Now, p = 3 x 5 x 7 = 105 

2. Value of q = 4 × 5 × 6 = 120

3.  Value of D + d = 3