Is the integer k greater than 3 ?

St1: The sum of -4 and k equals the square of an integer.

Minimum value of a perfect square = 0.
-4 + k = 0
k = 4.
For the sum to be any other perfect square, k will always be greater than 4.
Sufficient.

St2: k equals the square of an integer.

Minimum value of a perfect square = 0.
k can be 0 or any other perfect square.
Not sufficient.

Answer (A).

1.
The square of an integer must be positive. K-4>0 => K>4. sufficient.

2.
K is the square of an integer. 0^2, 1^2 < 3 and the square of any integer larger or equal to 2 >3
Insufficient.

Answer should be A.

Posted from my mobile device

Hello MarkusKarl,

Your approach is correct.

May I suggest a quick clarification?

The square of an integer must be non-negative since 0 is also a square of an integer, 0. In fact, 0 is the minimum value of a perfect square.

Ah, thanks! I keep forgetting which categories 0 is in. Its even and neither - or + right?

Posted from my mobile device

Indeed. 0 is even and neutral.

The problem looks very simple while solving here.
However while taking the GMAT PREP 6 I completely misunderstood the problem and got wrong answer....
Can someone post question links for similar kind of data sufficiency problem?
Thanks in advance........
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HI Bunuel, gmat1393

Can you pls tag as GMATPrep EP2

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Easy peasy
Minimum value of a perfect square = 0.
-4 + k = 0
k = 4.
For the sum to be any other perfect square, k will always be greater than 4.
Sufficient.

St2: k equals the square of an integer.

Minimum value of a perfect square = 0.
k can be 0 or any other perfect square.
Not sufficient.

Answer (A).
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Asked: Is the integer k greater than 3 ?

(1) The sum of -4 and k equals the square of an integer.
-4 + k = I^2 where I is an integer
smallest I =0
-4 + k >= 0
k>=4
k>3
SUFFICIENT

(2) k equals the square of an integer.[/quote]
k= I^2 where I is an integer
Smalles I = 0
k>=0
NOT SUFFICIENT

IMO A

I got stuck with this -

Statement 1: Assuming '1' as perfect square, K - 4 = 1; K= 3. In this case, K is = 3 and not greater. So I answered 'E' in this question.

If k - 4 = 1, then k = 5, not 3.
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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 k > 3.

Second and the third step of Variable Approach: From the original condition, we have 1 variable (k). 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 the sum of -4 and k equals the square of an integer.

=> Minimum value of a perfect square is '0'. Hence, to get sum (-4 + k) as '0', k has to be 4.

=> Is k greater than 3 - YES

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


Condition(2) tells us that the k equals the square of an integer.

=> minimum perfect square = 0 => k = 0 - Is k greater than 3 - NO

=> 4 => k = 2 - Is k greater than 3 - NO

=> 9 => k = 3 - Is k greater than 3 - NO

=> 16 => k = 4 - Is k greater than 3 - 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

Stmt 1: -4 + k = x^2. Squares are always positive therefore for this statement to be true, k has to be +ve and with a magnitude greater than 4. That automatically means anything >3. Sufficient.

Stmt 2: Doesn't help much. If K= 1^2, K < 3.
but if k= 4^2, then K > 3.
No unique solution can be reached. B insufficient.

answer: A

(1) says that "The sum of -4 and k equals the square of an integer": -4 + k = integer^2

(2) says that "k equals the square of an integer": k = integer^2

If k = 4 = intgerr^2, then -4 + k = = 0 = integer^2. So, the statements do not contradict, k can be 4 (in fact k = 4 is the only value that satisfies both statements).
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