UPSC Prelims 2019·CSAT·Quantitative Aptitude·Arithmetic

Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is

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Last updated 23 May 2026, 3:31 pm IST
  1. A13
  2. B15
  3. C16
  4. D30Correct

Explanation

Here's a brief explanation: 1. **Find L1 (Length of the first piece):** The three single-digit odd prime numbers are 3, 5, and 7. Their average = (3 + 5 + 7) / 3 = 15 / 3 = 5. So, L1 = 5. 2. **Set up equations for L2 and L3:** * From the third statement: L3 = L1 + L2 * From the second statement: L2 = L1 + (1/3)L3 3. **Solve for L2 and L3:** * Substitute L1 = 5 into the equations: L3 = 5 + L2 (Equation 1) L2 = 5 + (1/3)L3 (Equation 2) * Substitute Equation 2 into Equation 1: L3 = 5 + (5 + (1/3)L3) L3 = 10 + (1/3)L3 L3 - (1/3)L3 = 10 (2/3)L3 = 10 L3 = 10 * (3/2) = 15 * Now find L2 using L2 = 5 + (1/3)L3: L2 = 5 + (1/3)*15 L2 = 5 + 5 = 10 4. **Calculate the total length:** The lengths of the three pieces are L1 = 5, L2 = 10, and L3 = 15. The length of the original sheet = L1 + L2 + L3 = 5 + 10 + 15 = 30. Therefore, the length of the original sheet of paper is 30. The final answer is D.
Quantitative Aptitude: Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit
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