Question

xy, pq, yx and qp are two-digit numbers where x, y, p, and q are all numerals not necessarily distinct. Given that, (xy) × (pq) > (yx) × (qp) and [(xy) × (pq)] – [(yx) × (qp)] < 100. If last two digits of the product (xy) × (pq) are 8 and 3 (in ten’s and unit’s places respectively), then what are the last two digits of the product (yx × qp)?
1. 8 and 4
2. 2 and 5
3. 6 and 4
4. 2 and 6

Answer 1

Correct Answer - Option 1 : 8 and 4

Calculation:

⇒ (xy) × (pq) – (yx) × (qp)

⇒ (10x + y) (10p + q) – (10y + x)(10q + p)

⇒ 99(xp – yq)

⇒ Since 99(xp – yq) < 100 (as per the given condition)

∴ (xy) × (pq) – (yx) × (qp) = 99

⇒ (yx) × (qp) = (xy) × (pq) – 99

⇒ Now since the product (xy) × (pq) ends with 8 and 3, therefore

⇒ (yx) × (qp) must end with 8 and 4.