UPSC Prelims 2023 · CSAT
Question 79: Logical Reasoning and Mental Ability
A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct ?
- 1.There are exactly 15 small cubes with no paint on any face.
- 2.There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.
Select the correct answer using the code given below :
AnswerUPSC’s answer is (a).
The cuboid has 105 unit cubes. Unpainted cubes lie inside: (7 - 2) x (5 - 2) x (3 - 2) = 5 x 3 x 1 = 15, so statement 1 is true. Blue (7 x 3) and green (5 x 3) faces meet along the four edges of length 3. Each such edge has 3 cubes, but the two end cubes also touch a red face, leaving 1 cube with exactly blue and green. That gives 4 x 1 = 4 cubes, not 6, so statement 2 is false.
- 1. The inner block is 5 x 3 x 1 = 15 cubes.
- 2. Four edges of length 3 each give one blue-green cube, so 4 in all.
How you could have got this
- If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: The inner block is 5 x 3 x 1 = 15 cubes.
- Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: Four edges of length 3 each give one blue-green cube, so 4 in all.
Only (a) is left. This one needs every statement.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Right: 15 unpainted cubes, but only 4 blue-green cubes.
- (b) Wrong: statement 2 gives 4 cubes, not 6.
- (c) Wrong: statement 2 is false.
- (d) Wrong: statement 1 is true.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.