IPA IP 2022 Question 93

Topic: Basic Theory

A question IPA Japan published in 令和4年度 ITパスポート試験 公開問題 問93, translated into English. ITPEC is based on the same exams.

When the long side of a sheet of A3-size paper is folded in half, it becomes the size of A4, and the ratio of short side : long side does not change. Approximately how many times the long side of A4 size is the long side of A3 size?

Explanation

1.41 — the ratio that survives folding in half is 1 : √2, and the long side of A3 is the long side of A4 times √2.

Let A3 be s (short side) by l (long side). Folding the long side in half gives A4, whose sides are l ÷ 2 and s: its short side is l ÷ 2 and its long side is s.

  • •Same ratio of short side to long side: s ÷ l = (l ÷ 2) ÷ s
  • •So l2 = 2s2, and l ÷ s = √2
  • •A3’s long side ÷ A4’s long side = l ÷ s = √2 ≈ 1.41

Check with the real sizes: A3 is 297 × 420 mm and A4 is 210 × 297 mm, and 420 ÷ 297 ≈ 1.41.

Answer (a)

Why not others:

  • •(b) 1.5 — not a ratio that keeps the shape when halved; with sides in a ratio of 1.5 the halved sheet would be a different shape
  • •(c) 1.73 — that is √3, not √2
  • •(d) 2 — doubles the area, not the length of a side: A3 has twice the area of A4, but each side grows only by √2

Key rule: When halving a rectangle keeps its shape, its sides are in the ratio 1 : √2; each step up the A series multiplies the area by 2 and each side by √2.

Basic Theory · AI-written, may contain errors

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This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.