If a = 3.78xy7 and b = 1.37486, where x and y are positive digits, wha

Question

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

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GMATWhizTeam · Answer

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.

sambitspm · Answer

This one is not as straight-forward as it seems. See the attachment.

If a = 3.78xy7 and b = 1.37486, where x and y are positive digits, wha

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