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The given question consists of three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and answer the question. What will be the sum of two numbers? I. Among the two numbers, the largest number is greater than the smallest number by 4. II. 30% of the smallest number is equal to 20% of the largest number. III. The ratio between half of the largest number and one fourth of the smallest number is 3 ∶ 2.

The given question consists of three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and answer the question. What will be the sum of two numbers? I. Among the two numbers, the largest number is greater than the smallest number by 4. II. 30% of the smallest number is equal to 20% of the largest number. III. The ratio between half of the largest number and one fourth of the smallest number is 3 ∶ 2. Correct Answer Any two statements are required to answer the question.

Let the required number be x and y, where x > y

Considering statement I and II together,

From statement I,

⇒ x – y = 4 ---- (i)

From statement II,

⇒ (20/100)x = (30/100)y

⇒ 2x – 3y = 0 ---- (ii)

Solving equations (i) and (ii), we get

x = 12 and y = 8

∴ Statements I and II are sufficient together to answer the question.

Considering statement I and III together,

From statement I,

⇒ x – y = 4 ---- (i)

From statement III,

⇒ (1/2)x ∶ (1/4)y = 3 ∶ 2

⇒ 4x – 3y = 0 ---- (ii)

Solving these equations,

x = -12 and y = -16

∴ Statements I and III are sufficient together to answer the question.

Considering statement II and III together,

From statement II,

⇒ (20/100)x = (30/100)y

⇒ 2x – 3y = 0 ---- (i)

From statement III,

⇒ (1/2)x ∶ (1/4)y = 3 ∶ 2

⇒ 4x – 3y = 0 ---- (ii)

Solving these equations,

x = 0 and y = 0

∴ Statements II and III are sufficient together to answer the question.

∴ Any two statements are required to answer the question.

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