Direction The following question has three statements Study the question and the statements and deci...........

Quantitative Aptitude (SBI-PO) Data Sufficiency

Direction: The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

What is the ratio of the volume of the cube to the volume of the cuboid?

I. The Total Surface Area of the cuboid is 352 cm2 and the ratio of the length, breadth and height of the cuboid is 3:2:1.

II. The Total Surface Area of the cube is 726 cm2.

III. The length of the cuboid is 1.5 times of the breadth of the cuboid and 3 times of the height of the cuboid. The difference between the height and the length of the cuboid is 8 cm.

Any two of the statements

All the statements

II and III together

I and II together

Either statement I and II or statement II and III

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Explanation:

Statement I: Total Surface Area of cuboid

= 2 (lb + bh + hl) Let length = 3x, breadth = 2x, height = x ∴ 352 = 2 (3x × 2x + 2x × x + x × 3x) ⇒ 176 = (6x² + 2x² + 3x²) ⇒ 176 = 11x² ⇒ x² = 16 ⇒ x = 4

∴ Length = 12 cm, Breadth = 8 cm, Height = 4 cm Volume = lbh ⇒ 12 × 8 × 4 = 384 cm3

Statement II: Total Surface Area of cube = 6s2

∴ 726 = 6s² ⇒ s² = 121 ⇒ s = 11 cm

Volume of the cube = s³ ⇒ 113 = 1331 cm³

Statement III: Let height of the cuboid = x cm, length = 3x, breadth = 2x Difference = 3x – x ⇒ 8 = 2x ⇒ x = 4 ∴ length = 12 cm, breadth = 8 cm, height = 4 cm

Volume of the cuboid = lbh ⇒ 12 × 8 × 4 = 384 cm³

∴ Either statement I and II or statement II and III are required to answer the question.