If m and n are positive decimals smaller than 1, is m + n 1?

Question

If m and n are positive decimals smaller than 1, is  m+n>1 ?

(1) All decimal digits of m and n are greater than 5

(2)  mn > \frac{1}{2}

$!vakumar.m · Answer

If m and n are positive decimals smaller than 1, is m+n>1?
i.e, m and n lie between 0 and 1
(1) All decimal digits of m and n are greater than 5
Sufficient. Because both m and n are greater than 0.5
so, m+n > 1
(2) mn>1/2
This is possible only when both m and are greater than 0.5
Hence, sufficient
Answer D

keepgoingmarvel · Answer

(1) If both m & n are 0.5 then m+n=1 & not >1, does it not make it insufficient?

Bunuel · Answer

Notice that the statement says all decimal digits are  greater  than 5, so neither m nor n can be 0.5. The smallest possible value for each is 0.6, which means m + n must be greater than 1.

P.S. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

Saksham23 · Answer

In the 2nd st, if I give m = 0.6 and n = 0.6, that results in 0.36 but 0.6 + 06. = 1.2 which is greater than 1 ? 
How do we say that 2nd st is sufficient on it's own ?

Bunuel · Answer

For (2), m = 0.6 and n = 0.6 is  not  a valid test case because it gives mn = 0.36, which does  not  satisfy the statement mn > 1/2. When testing a statement, you must choose values that meet  both  the conditions of the question stem (m and n are positive decimals less than 1)  and  the statement being tested (mn > 1/2). Any such valid pair will always give m + n > 1, so Statement (2)  is sufficient .

If m and n are positive decimals smaller than 1, is m + n > 1?

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