In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don't know which letter represent which number. Consider the following relationships:

i. a + c = e
ii. b – d = d
iii. e + a = b

Question

In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don't know which letter represent which number. Consider the following relationships:

i. a + c = e
ii. b – d = d
iii. e + a = b

Accepted Answer

a = 4, e = 6 — a + c = e ... (i) b &ndash; d = d b = 2d ... (ii) e + a = b ... (iii) From (ii), we get, Either b = 4 and d = 2 or b = 10 and d = 5 From (i) and (iii), we get, 2a + c = b ... (iv) &there4; b = 4 can easily be eliminated because there is no value of b that will satisfy equation (iv). &there4; b = 10 and d = 5 a = 4 or 6 and e = 6 or 4, but c = 2 Using equation (i), we have, a = 4 and e = 6 Hence, option (b).

CAT 2001 — QA Question 43

Answer & solution

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