Kimberly77 wrote:
BrentGMATPrepNow wrote:
jlgdr wrote:
If x < 12, then it must be true that
(A) -x < -12
(B) -x - 2 < 14
(C) -x + 2 < -10
(D) x + 2 < 10
(E) x - 2 < 11
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test values that satisfy the given inequality.
From here, I'll give myself 15-20 seconds to identify a faster approach.....
We can also solve the question by analyzing each answer choice to see if it adheres to the given inequality algebraically, but since I'm less likely to make mistakes testing values, I'll go that routeWhen looking for a value to test, I typically start with 0, since it's such an easy value to work with. Since it turns out that
x = 0 is solution to the inequality x < 12, let's plug
x = 0 into each answer choice to see if it's a solution:
(A) -
0 < -12, which simplifies to 0 < -12. Not true. Eliminate A.
(B) -
0 - 2 < 14, which simplifies to -2 < 14. True. KEEP.
(C) -
0 + 2 < -10, which simplifies to 2 < -10. Not true. Eliminate C.
(D)
0 + 2 < 10. True. KEEP.
(E)
0 - 2 < 11. True. KEEP.
We're down to choices B, D and ENow let's test an "extreme" possible value that satisfies the inequality x < 12
We can choose a value close to 12 (like x = 11.5) or a value far away (like x = -20)
Let's test
x = 11.5, by plugging it into the remaining three answer choices:
(B) -
11.5 - 2 < 14, which simplifies to -13.5 < 14. True. KEEP.
(D)
11.5 + 2 < 10. Doesn't work. Eliminate D
(E)
11.5 - 2 < 11. True. KEEP.
We're down to choices B and ENow let's test another extreme value,
x = -20:
(B) -
(-20) - 2 < 14, which simplifies to 18 < 14. Doesn't work. Eliminate B
(E)
-20 - 2 < 11. True. KEEP.
Answer: EGreat explanation
BrentGMATPrepNow. In regard to D, if solving as x + 2 < 10 --> x<8. This mean the greatest of x will only be 7. Not sure why is this not true?
E, x<13 which mean x could be 12, isn't this go against given x <12 ? Thanks Brent
You are reading the question backwards.
We are told that x < 12. This part is
guaranteed.
This means x COULD equal values such as 8, 11.5, 7, 0, -500, 11.999999, 5, 4.1, etc.
Given this wide range of possible x-values, we're looking for an answer choice that is must be true for all possible values of x (i.e., 8, 11.5, 7, 0, -500, 11.999999, 5, 4.1, etc.)
(D) x + 2 < 10
When we simplify D, we get x < 8.
Given all of the possible values of x (i.e., 8, 11.5, 7, 0, -500, 11.999999, 5, 4.1, etc.), must it be true that x < 8?
No.
Notice that, among the possible values of x, we have numbers like 8, 11.5 and 11.999999, all of which are larger than x.
So we certainly can't conclude that x MUST be less than 8.
(E) x - 2 < 11
When we simplify E, we get x < 13.
Given all of the possible values of x (i.e., 8, 11.5, 7, 0, -500, 11.999999, 5, 4.1, etc.), must it be true that x < 13?
Yes.