Child Photograph Rows

CAT 2006 Slot 1 · QA · Medium · Quantitative Aptitude

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A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

  1. A.

    3

  2. B.

    4

  3. C.

    5

  4. D.

    6

  5. E.

    7

Answer

6

Explanation

Let nn be the number of rows and xx be the number of children in the front row. Total children Sn=n2[2x−(n−1)3]=630S_n = \frac{n}{2}[2x - (n-1)3] = 630. Test options for nn:

  • n=3  ⟹  3x−9=630  ⟹  3x=639  ⟹  x=213n = 3 \implies 3x - 9 = 630 \implies 3x = 639 \implies x = 213 (Integer, possible).
  • n=4  ⟹  4x−18=630  ⟹  4x=648  ⟹  x=162n = 4 \implies 4x - 18 = 630 \implies 4x = 648 \implies x = 162 (Integer, possible).
  • n=5  ⟹  5x−30=630  ⟹  5x=660  ⟹  x=132n = 5 \implies 5x - 30 = 630 \implies 5x = 660 \implies x = 132 (Integer, possible).
  • n=6  ⟹  6x−45=630  ⟹  6x=675  ⟹  x=112.5n = 6 \implies 6x - 45 = 630 \implies 6x = 675 \implies x = 112.5 (Not an integer, IMPOSSIBLE).

Thus, 6 rows is not possible.

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