Question:
In some code, letters a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. We just do not know which letter represents which number. Consider the following relationships:
a + c = e,
b – d = d and
e + a = b
Which of the following statements is true?
(A) b = 4, d = 2
(B) a = 4, e = 6
(C) b = 6, e = 2
(D) a = 4, c = 6
Answer:
(B) a = 4, e = 6 is the correct answer.
Explanation:
(A) b = 4, d = 2
a + c = e => a + c = e
b – d = d => 4 - 2 = 2
e + a = b => e + a = 4
We are not able to find out what will be at place of a , c , e by which all other relationships are not getting satisfied. And if we apply numbers by hit and trial they are not getting satisfied.
(B) a = 4, e = 6
a + c = e => 4 + c = 6 => 4 + 2 = 6
b – d = d => b - d = d => 10 - 5 = 5
e + a = b => 6 + 4 = 10
We were able to find all a , b , c , d , e and it satisfies all relationships given.
(C) b = 6, e = 2
a + c = e => a + c = 2
b – d = d => 6 - d = d
e + a = b => e + a = 6
We are not able to find out what will be at place of a , c , d by which all other relationships are not getting satisfied. And if we apply numbers by hit and trial they are not getting satisfied.
(D) a = 4, c = 6
a + c = e => 4 + 6 = 10
b – d = d => b - d = d
e + a = b => e + 4 = b => 10 + 4 = 14(this is not from the numbers as given in question so b can't be equal to 14)
We got stuck at the value of b which was 14 and not given in question so, we can leave this option in between as it is not satisfying the relationships.
Therefore, (B) a = 4, e = 6 is the correct answer.
