In a division problem, the divisor is 4 times the quotient and 2 times the remainder. If the remainder is 32, then find the dividend.

Correct — D. Start from the remainder, the one number the stem gives outright.

Divisor = 2 × remainder = 2 × 32 = 64
Quotient = divisor ÷ 4 = 64 ÷ 4 = 16
Dividend = divisor × quotient + remainder = 64 × 16 + 32
= 1,024 + 32 = 1,056 → option (d).

Why the others are wrong

• (a)
  1065 — 1065 is 1056 with its last two digits swapped. Divide it by 64 and the quotient is 16 with remainder 41, and 41 is not the 32 given.
• (b)
  3240 — 3240 divided by 64 leaves quotient 50, remainder 40. The quotient has to be a quarter of the divisor, which is 16, so this dividend is far too big.
• (c)
  1650 — 1650 divided by 64 leaves quotient 25, remainder 50. The divisor must be twice the remainder, and 64 is not twice 50.

Every division statement is one identity: Dividend = Divisor × Quotient + Remainder.

The stem chains three of those four numbers to each other — the divisor is 4 times the quotient and 2 times the remainder — so pinning any one of them pins the rest. The remainder is handed to you as 32, which makes the divisor 64 and the quotient 16.

A legal division also needs the remainder to be smaller than the divisor. Here 32 < 64, so the data describe a real division and the dividend is 64 × 16 + 32 = 1,056.

Key facts

• Division algorithm: Dividend = Divisor × Quotient + Remainder, with 0 ≤ Remainder < Divisor.
• Divisor = 2 × 32 = 64 and quotient = 64 ÷ 4 = 16.
• Dividend = 64 × 16 + 32 = 1,056.
• The remainder 32 is smaller than the divisor 64, so the stated data are consistent.

Common traps

• Reading 'the divisor is 4 times the quotient' backwards and taking the quotient as 256
• Multiplying divisor by quotient and forgetting to add the remainder, which gives 1,024
• Picking 1065, whose final two digits are those of 1056 in the wrong order

No directly related past PYQ was found.