GMAT Hard Math Practice Question 29

The given question is a challenging GMAT quant problem solving question testing concepts in number properties. Concepts covered: Number properties, Polynomials, Exponents, and Real Numbers.

Question 29: If a, b, .. , j are real numbers such that (a - 1)² + (b - 2)⁴ + (c - 3)⁶ + ... + (j - 10)²⁰ = 0, what is the value of b × d × f × h × j ?

1. 120
2. 36,28,800
3. 3840
4. 240
5. 1536

Video Explanation

Explanatory Answer | GMAT Number Properties

Because square of real numbers cannot be negative, sum of even powers of real numbers can be zero only if each of the terms is zero.

Therefore, (a - 1) = 0, (b - 2) = 0, ..., (j - 10) = 0
Or a = 1, b = 2, c = 3, .... j = 10

b × d × f × h × j = 2 × 4 × 6 × 8 × 10
= 2⁵ × (1 × 2 × 3 × 4 × 5)
= 32 × 120
= 3840

Choice C is the correct answer.