Bunuel
If a = 3.78xy7 and b = 1.37486, where x and y are positive digits, what is the value of a + b?
(1) If a and b are rounded to nearest thousandths digit, then a + b = 5.162
(2) If a and b are rounded to nearest ten-thousandths digit, then a + b = 5.1622
Solution
Step 1: Analyse Question Stem
• \(a = 3.78xy7\)
• \(b = 1.37486\)
• \(0 < x ≤ 9\)
• \(0 < y ≤ 9\)
• We need to find the value of a + b
o We can find exact value of a + b only if we know x and y.
Therefore, we basically need to find x and y.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: If a and b are rounded to nearest thousandths digit, then a + b = 5.162
• b rounded to its thousandths place \(= 1.375\)
• Thus, a rounded to its thousandths place \(= 5.162 - 1.375 = 3.787\)
• Since, a is rounded to it’s thousandths place, so there can be two cases as given below:
o Case 1 : If \(y < 5\), then \(a = 3.78x = 3.787 ⟹ x = 7\)
o Case 2: If \(y ≥ 5\), then then \(a = 3.78(x+1) = 3.787 ⟹ x = 6\)
• So, from this statement, we can neither find exact value of x nor the value of y.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: If a and b are rounded to nearest ten-thousandths digit, then a + b = 5.1622
• b rounded to its ten-thousandths place = 1.3749
• Thus, a rounded to its ten-thousandths place = 3.78x(y+1) = 5.1622 - 1.3749 = 3.7873
o This means, \(x = 7\) and \(y = 2\)
• Since we got x and y we can now easily find a+b.
Hence, statement 2 is sufficient.
Thus, the correct answer is
Option B.