Is x 10 ? (1) x - 5 10 (2) x +5 10

Question

Is x > 10 ?

(1) x - 5 > 10
(2) x +5 > 10

Why is the answer statement 1 alone sufficient and not both statements together sufficient?
Both statements together is x>15 and x>5 --> upon overlapping the sets it gives x>15?

ElevateR · Answer

Statement 1: x-5>10
x>15
x is set with values greater than 15 ALWAYS, which  also means X is always greater than 10 
(1) SUFFICIENT

Statement 2: x+5>10
x>5
x is a set of values which may be greater than 10 or less than 10.
(2) NOT SUFFICIENT

When you take both the statements together, you eventually get the same result as in case of statement 1, therefore statement 2 doesn't add anything new to the result. Therefore the ans is  A 
Also in case of DS questions, as soon as we get any sufficient statement , we remove options C and E from the answer options.

GMATinsight · Answer

NidhiR

Just commenting on highlighted part

When you know that statetement 1 alone is SUFFICIENT then immediately croos options B, C and E therefore there is no scope of even planning to combine statements then,

Kinshook · Answer

Hi  NidhiK5 
Asked: Is x>10?
1) x-5>10 --> x>15
Take any number x>15 and it will satisfy x>10
SUFFICIENT

2) x+5>10 --> x>5
Take x = 6; x<10
Take x = 17; x>10
NOT SUFFICINET

IMO A

Statement 2 is NOT SUFFICIENT since it gives different results and x>10 is not always satisfied.

Hope it helps!

tuan1995 · Answer

A is the answer

(1) x - 5 > 10
hence x>15 ---> sufficient

(2) x +5 > 10
then x>5 ---> insufficient since x can be greater than 10 or smaller than 10

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.

Since it a key question [INTEGER QUESTION]you know the Variable Approach, you can sit back and relax when you go to take an exam.

The answer could be A, B, or D, but the default answer is D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question. We have to find whether x > 10.

Second and the third step of Variable Approach: From the original condition, we have 1 variable (x). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take a look at each condition.

Condition(1) tells us that the x - 5 > 10.

=> x - 5 > 10

=> x > 15

So, the range if x will be greater than 15 and 10 is less than 15.

=> Is x greater than 10 - YES

=>Since the answer is unique YES, condition(1)is sufficient by CMT 1.

Condition(2) tells us that the x + 5 > 10.

=> x + 5 > 10

=> x > 5

=> If x = 7 or 8 or 9 or 10 - Is x greater than 10 - NO

=> If x = 11 or 12 .. - Is x greater than 10 - YES

Since the answer is not unique YES or NO, condition(2) is not sufficient by CMT 1.

Condition(1) alone is sufficient.

So, A is the correct answer.

Answer: A

Rogermoris · Answer

x - 5 > 10, hence x>15 
Which means 1st statement is sufficient

x +5 > 10, hence x>5 
Which is insufficient since x can be greater than 5, i.e 6,7,8....

Hence option   is the answer

bumpbot · Answer

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Is x > 10 ? (1) x - 5 > 10 (2) x +5 > 10

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