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Question

What is the sum of two numbers?

I. The bigger of these two numbers is 6 more than the smaller number.

II. 40% of the smaller number is equal to 30% of the bigger number.

III. The ratio between half of the bigger number and one-third of the smaller number is 2:1.

(A) II And III Are Sufficient.

(B) Only I And II Are Sufficient.

(C) Only II And III Are Sufficient.

(D) I And Either II Or III Are Sufficient.


A

Option (D) is correct.

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B

Options (A), (b), and (C) are incorrect.

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Solution

The correct option is A

Option (D) is correct.


Step 1. Solve the first given statement.

I. It is given that the bigger of these two numbers is 6 more than the smaller number.

Consider the two numbers be x and y such that y>x.

y=x+61

Step 2. Solve the second given statement.

II. It is given that 40% of the smaller number is equal to 30% of the bigger number.

40%ofx=30%ofy40100·x=30100·yxy=34

4x=3y2

Step 3. Solve the third given statement.

III. It is given that the ratio between half of the bigger number and one-third of the smaller number is 2:1.

12y:13x=2:13y2x=21xy=34

4x=3y3

Step 4: Determine the sum of two numbers.

Substitute the value of y from 1 into 2.

4x=3x+64x=3x+184x-3x=18x=18

Substitute the value of x into 1.

y=18+6y=24

The sum of two numbers is 18+24=42.

Hence, option (D) is correct.


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