One number is not like the others: 1331, 2197, 3375, 4096
- (a)1331
- (b)3375
- (c)4096
- (d)2197
Answer
Why
Correct — C. Take the cube root of each number.
Rule: cubes of the odd numbers 11, 13, 15.
1331 = 11³
2197 = 13³
3375 = 15³
4096 = 16³, the cube of an even number.
Parity and squares agree: 4096 is the one even number of the four, and it is also 64², a perfect square. So 4096, option (c), is the odd one out.
Why the others are wrong
- (a)1331 — 1331 = 11³, an odd number cubed, like 13³ and 15³. It also reads the same backwards, but that is a surface feature; its cube root puts it in the group.
- (b)3375 — 3375 = 15³. 15 is odd, so 3375 sits in the odd-cube group with 1331 and 2197.
- (d)2197 — 2197 = 13³ (13 × 13 = 169, × 13 = 2197). It fills the gap between 11³ and 15³ in the odd-cube group.
Concept
Four-digit numbers in an odd-one-out can hide powers. If you know the cubes of 11 to 20 by sight, this becomes recognition, not calculation.
Here all four numbers are cubes, so 'is it a cube?' separates nothing. The next layer is the cube roots: 11, 13 and 15 are odd, 16 is even.
An odd-one-out can have more than one defensible rule, so the safe reading is the one where every rule agrees.
Here they do. 4096 is the only even number of the four, and it is the only perfect square, 64². Either route reaches option (c).
Key facts
- 11³ = 1331, 13³ = 2197, 15³ = 3375, 16³ = 4096.
- 4096 = 16³ = 64² = 2¹².
- An odd number cubed is odd, and an even number cubed is even.
Study next
Common traps
- Stopping at 'all four are cubes' and guessing, instead of comparing the cube roots.
- Picking 1331 because it reads the same backwards, when the cube roots give a rule for all four.
Cubes also drive 17 Sep 2025, 16:00, Reasoning Q.9, where 1331, 10648, 35937, 85184 are 11³, 22³, 33³, 44³ and the next term is 55³ = 166375.
At 11 Sep 2024, 09:00, Reasoning Q.21, 8 → 512 and 12 → 1728 are cubes, so 15 → 3375, the same 15³ as here.
Related PYQs
No directly related past PYQ was found.