If |x| > 3, Which if the Following Must be True? GMAT Problem Solving

Question: If |x| > 3, which if the following must be true?

1. x > 3
2. \(x^9\) > 9
3. |x-1| > 2

1. I only
2. II only
3. I and II only
4. II and III only
5. I, II and III

“If |x| > 3, which if the following must be true?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution (1):

If |x| > 3, then it must be true that either x > 3 or x < -3
(1) x > 3
This need not to be true, since it’s also possible that x < -3
For example, c could be equal -5
So, statement I need not be true
Eliminate answer choice A, C and E
Important: The remaining two answer choices (B and D) both state that statement II is true.

So, we need not analyze statement II, since we already know it must be true.
That said let’s analyze it for “fun”

(2) \(x^2\) > 9

This means that Either x > 3 or x < -3
Perfect – this matches our original conclusion that Either x > 3 or x < -3

(3) |x-1| > 2

Let’s solve two cases:
Case a) x – 1 > 2, which means x > 3 PERFECT
Or
Case b) x – 1 < -2, which means x < -1
Must it be true that x < -1?
YES.
We already learned that Either x > 3 OR x < -3
If x < -3, then we can be certain that x < -1

So, statement 3 must also be true.

Correct Answer: D

Approach Solution (2):

Original statement |x| > 3, which means either x > 3 or x < -3
Now check the options

Option 1: x > 3 – not always true as x can be smaller than -3
Thus options A, C and E are ruled out. Only B and D are left.

Option 2: \(x^2\) > 9 – Always true for x > 3 or x < -3

To check – if x = 4,5,6,7… or -4,-5,-6,-7
\(x^2\) > 9

Option 3: |x-1| > 2
Which means (x – 1) > 2
x > 3 (if x -1 > 0) – True
It also means (x -1) < -2
x < -1 (if x – 1 < 0)
x < -1 satisfies x < -3. Thus this is true

both 2 and 3 is true.

Correct Answer: D

Suggested GMAT Problem Solving Questions

• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If 298=256L+N298=256L+N , Where L and N are Integers and 0≤N≤40≤N≤4 , What is the Value of N? GMAT Problem Solving
• How Many 5-Letter Words can be Formed Using the Letters of the English Alphabet that Contain 2 Different Vowels GMAT Problem Solving
• If a+b+c = 0 and a^3+b^3+c^3 = 216, What is the Value of a∗b∗c ? GMAT Problem Solving
• If a Polygon has 44 Diagonals, Then How Many Sides are There in the Polygon? GMAT Problem Solving
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), For Every n≥1, Then a11 Equals GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• A Container in the Shape of a Right Circular Cylinder is 1/2 Full of Water. GMAT Problem Solving
• How Many Multiples of 7 are there Between 21 and 343, Exclusive? GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
• How many Terminating Zeroes does 200! Have? GMAT Problem Solving
• 1511−151014=? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving
• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving