If 2x q - 10 and |q|

Question

If 2x > q - 10 and |q| < 4, which of the following CANNOT be a value of x?

(A) −7
(B) −6
(C) −5
(D) −4
(E) −3

Amirbek · Answer

Hi!
I think the answer should be A and NOT E.

If we put -7 into the equation we will get q<-4, which will not satisfy |q| < 4

Dream009 · Answer

This is experts global answer key - so it has to be correct

paragw · Answer

They might be wrong in this case coz I don't see any trap in this question as of now

Given |q| < 4, q must lie between −4 and 4, so q − 10 lies between −14 and −6.
 The inequality 2x > q − 10 will be satisfied for some allowed value of q only if 2x is greater than −14.
 This requires x > −7.
So x = −7 cannot satisfy the condition, but all other options are greater than −7 and can work for some value of q.

VrushilGala · Answer

2x > q - 10
If we plug in x = -7
-14 > q - 10
-4 > q
|q| < 4, so q can take all the values ranging from -3 to 3
-4 > q can’t be satisfied. Answer should be (A) -7

Let’s check the given answer (E) -3
-6 > q - 10
4 > q
q can take values ranging from -3 to 3 to satisfy this condition.
The answer key is wrong.
Correct answer should be (A) -7

Bunuel · Answer

Edited the OA from E to A. Thank you all!

tam28 · Answer

|q|<4 => -4 -14 (-14/2)<(q-10)/2<(-6/2) => -7<(q-10)/2<-3 Lets call the quantity q(-10)/2 as p given 2x > q-10 => x > (q-10)/2 => x > p p can take the values (-7,-3) and since x is greater than p therefore x can not take the value -7

rajdeep212003 · Answer

I approached this by checking the smallest possible value q can take.

Given:

2x > q − 10
and |q| < 4

Since |q| < 4, q cannot be −4, but it can be very close to −4.
To keep it simple, I checked with q = −3.

Then:

2x > −3 − 10
2x > −13
x > −6.5

So x cannot be −7.

The other choices can work with suitable q values, but −7 is always too small.

Answer: (A) −7

I found it quicker to test the boundary value of q instead of trying to rearrange everything algebraically.

— Rajdeep

BongBideshini · Answer

|q| < 4 So, -4 < q < 4 2x > q - 10 => q < 2x + 10 ----(1) we know that , -4 < q. ----(2) using (1) + (2) -4 < 2x + 10 => 2x > -14 => x > -7 Ans (A)

ExpertsGlobal5 · Answer

A is the correct answer choice.

Video explanation:

https://www.youtube.com/watch?v=dDPF_Fo5BuM

MakB · Answer

Why not -3 (E)??
The range for (q-10)/2 is:
-7< (q-10)/2 < -3

If -7 cannot be the answer, so cant -3.

Bunuel · Answer

If 2x > q – 10 and |q| < 4, which of the following cannot be a value of x ?

A. -7
B. -6
C. -5
D. -4
E. -3

Since |q| < 4, we have:

-4 < q < 4

Subtract 10:

-14 < q - 10 < -6

We need:

2x > q - 10

Check x = -7:

2x = -14

But q - 10 is always greater than -14 ( -14 < q - 10 < -6), so x cannot be -7.

Thus, x cannot be -7.

Answer: A.

MakB

Why not -3 (E)??
The range for (q-10)/2 is:
-7< (q-10)/2 < -3

If -7 cannot be the answer, so cant -3.

We have:

-14 < q - 10 < -6

2x > q - 10

So x can be -3 for example, if q = 0.

If 2x > q - 10 and |q| < 4, which of the following CANNOT be a value

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