Is 2x - 3y < x^2 ? GMAT Data Sufficiency

Question: Is 2x - 3y < x^2 ?

(1) 2x - 3y = -2
(2) x > 2 and y > 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“Is 2x - 3y < x^2 ?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2022". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

We can rewrite the question
It is asked if 2X - 3Y < X^2. so we rewrite the question to ask if 2X < X^2 + 3Y. making this is a YES/NO question.
Statement 1 says
2X - 3Y = -2
We can rewrite it as
Is -2 < \(X^2\)?
With ALL conceivable values of X, the answer to the question is ALWAYS YES because \(X^2\)can be either 0 or any positive value.
Therefore statement 1 is sufficient
Statement 2 says
X > 2 and Y > 0
Since we are aware that X > 2.
2X will ALWAYS be < \(X^2\)
We also understand that Y > 0.
Therefore, (\(X^2\)+ 3Y) will increase as Y increases.
All of this provides proof that.
2X is ALWAYS < \(X^2\)+ 3Y. The answer is Always Yes.

EACH statement ALONE is sufficient.

Correct Answer: D

Approach Solution 2:

There is another approach to answering this question which is easier
Statement 1 says
2X - 3Y = -2
When we substitute the inequality
2x-3y<\(X^2\)
2<\(X^2\)or Is \(X^2\)>-2 ?
Yes! Because Square of any number is >=0
This is Sufficient
Statement 2 says
x>2 & Y>0
From statement 1 we know 2x-3y<\(X^2\)
We can say that 2x-\(X^2\)<3y or x(2-x)<3y
Now that we know that LHS will always be negative and RHS will always be positive, we can insert in the inequality x>2 and y>0 above.
This is Sufficient

EACH statement ALONE is sufficient.

Correct Answer: D

Approach Solution 3:

(1) 2x−3y=−22x−3y=−2 --> question becomes: is −2−2x2≥0>−2. Sufficient.

(2) x>2x>2 and y>0y>0 --> is 2x−3y is x(x−2)+3y>0x(x−2)+3y>0 --> as x>2x>2 then x(x−2)x(x−2) is a positive number and as y>0y>0 then 3y3y is also a positive number --> sum of two positive numbers is more than zero, hence x(x−2)+3y>0x(x−2)+3y>0 is true. Sufficient.

EACH statement ALONE is sufficient.

Correct Answer: D

Some suggested GMAT Data Sufficiency Questions

• In Triangle PQR, if PQ = x, QR = x + 2, and PR = y GMAT Data Sufficiency
• What is x? (1) x = 4y - 4 (2) xy = 8 GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle GMAT Data Sufficiency
• What is the Remainder when 333^222 is Divided by 7? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True? GMAT Data Sufficiency
• In the Figure Above, What is the Area of Semicircle DPA? GMAT Data Sufficiency
• Is |x-10| > |x-30| GMAT Data Sufficiency
• What is The Value of (a!+b!)(c!+d!)? GMAT Data Sufficiency
• If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency 
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency