Three of the following numbers are alike in a certain way and one is different. Pick the odd one out. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

Correct — D. Rule: the second number is the first divided by 5 and multiplied by 8 — the ratio 5 : 8.

65 ÷ 5 = 13, and 13 × 8 = 104
75 ÷ 5 = 15, and 15 × 8 = 120
90 ÷ 5 = 18, and 18 × 8 = 144

45 ÷ 5 = 9, and 9 × 8 = 72, but the pair shows 70.

Three pairs hold the ratio 5 : 8 and one misses it by 2, so option (d) is the odd one.

Why the others are wrong

• (a)
  65 – 104 — 65 : 104 reduces to 5 : 8 on dividing both by 13, the same ratio as the other two, so it belongs to the group.
• (b)
  75 – 120 — 75 : 120 reduces to 5 : 8 on dividing both by 15, so it matches rather than stands apart.
• (c)
  90 – 144 — 90 : 144 reduces to 5 : 8 on dividing both by 18, which is the shared rule, not the exception.

On an odd-one-out over number pairs, test a ratio before you test a difference. Ratios hold across pairs of very different size, while differences rarely do.

Here 104 over 65, 120 over 75 and 144 over 90 all come to 1.6, and 70 over 45 comes to about 1.56.

The quick field test is to multiply the first number by 8 and divide by 5. If the answer is the second number, the pair fits; 45 gives 72, not 70.

Key facts

• 65 : 104, 75 : 120 and 90 : 144 all reduce to 5 : 8.
• 45 in the ratio 5 : 8 would pair with 72, not 70.
• 8 over 5 is 1.6, so the second number is 1.6 times the first.

Common traps

• Testing differences first, which give 39, 45, 54 and 25 and prove nothing
• Rounding 70 ÷ 45 to 1.6 and passing the pair as a fit
• Splitting numbers into digits despite the question's note

No directly related past PYQ was found.