$$If\ 4x-12\ge x+9,$$ Which of the following must be true?
A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8
The OA is A.
Experts, to solve this PS question, can I isolate the x and get the answer, right?
$$3x\ge21$$
$$x\ge7$$
But why only A is true? What about C and D? Experts, any suggestion? Thanks in advance.
If 4x-12 >= x + 9, which of the following must be true?
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Hi LUANDATO,$$If\ 4x-12\ge x+9,$$ Which of the following must be true?
A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8
The OA is A.
Experts, to solve this PS question, can I isolate the x and get the answer, right?
$$3x\ge21$$
$$x\ge7$$
But why only A is true? What about C and D? Experts, any suggestion? Thanks in advance.
Let's take a look at your question.
$$4x-12\ge x+9$$
$$4x-12+12\ge x+9+12$$
$$4x\ge x+21$$
$$4x-x\ge x+21-x$$
$$3x\ge21$$
$$\frac{3x}{3}\ge\frac{21}{3}$$
$$x\ge7$$
The answer is x is greater than or equal to 7.
We can see that option B, C, D and E does not include x = 7.
Option A is x>6, which means in this interval x = 7 is included as well as values greater than 7.
Therefore, Option A is correct.
Does that make sense?
I am available if you'd like any follow up.
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Hi LUANDATO,
You've correctly defined the range of values that X could be (re: X could equal 7 or anything greater than 7). You have to remember to answer the question that is ASKED though; we're asked what MUST be true. Only one answer will contain all of the solutions that you are looking for (the other 4 answers ignore some or all of the solutions). No matter what value of X you choose from the given range, it will ALWAYS be greater than 6.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
You've correctly defined the range of values that X could be (re: X could equal 7 or anything greater than 7). You have to remember to answer the question that is ASKED though; we're asked what MUST be true. Only one answer will contain all of the solutions that you are looking for (the other 4 answers ignore some or all of the solutions). No matter what value of X you choose from the given range, it will ALWAYS be greater than 6.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Simplifying the inequality we have:LUANDATO wrote:$$If\ 4x-12\ge x+9,$$ Which of the following must be true?
A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8
4x - 12 ≥ x + 9
3x ≥ 21
x ≥ 7
If x is greater than or equal to 7, then it must be greater than 6. For example, if x = 7, we see that only answer choice A captures x = 7. No matter what value of x is chosen (as long as x ≥ 7), we are guaranteed that the value of x that has been chosen will indeed be greater than 6.
Answer: A
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