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Which of the following could be t if |5t – 8| < 1?

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by M7MBA » Sun Oct 29, 2017 7:10 am
Which of the following could be t if |5t - 8| < 1?

A. 5/8
B. 5/4
C. 5/3
D. 5
E. 10

The OA is C

Is the only way to solve this PS question trying option by option? Experts, could you give me another way to solve it?
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Answer

by EconomistGMATTutor » Sun Oct 29, 2017 8:42 am
Hello M7MBA.

You could try obtion by option but I will give you another way to solve it.

$$|5t-8|<1<=>-1<5t-8<1\ <=>\ 7<5t<9\ <=>\frac{7}{5}<t<\frac{9}{5}\ $$ $$ <=>\ 1,4\ <\ t\ <\ 1,8$$

Now, let's take a look at the options.

a) ------> 5/8<1,4 INCORRECT.
b) ------> 5/4=1,22... <1,4 INCORRECT.
c) ------> 5/3=1,66... CORRECT.
d) ------> 5>1,8 INCORRECT.
e) ------> 10>1,8 INCORRECT.

So, the answer is C.

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
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Re: Which of the following could be t if |5t – 8| < 1?

by Scott@TargetTestPrep » Thu Jan 23, 2020 10:59 am
M7MBA wrote: ↑
Sun Oct 29, 2017 7:10 am
 Which of the following could be t if |5t - 8| < 1?

A. 5/8
B. 5/4
C. 5/3
D. 5
E. 10

The OA is C

Is the only way to solve this PS question trying option by option? Experts, could you give me another way to solve it?
When (5t - 8) is positive, we have:

5t - 8 < 1

5t < 9

t < 9/5 = 1.8

When (5t - 8) is negative, we have:

-(5t - 8) < 1

-5t + 8 < 1

-5t < -7

t > 7/5 = 1.4

Combining the two inequalities, we ge 1.4 < t < 1.8. Thus, t could be 5/3 (which is roughly 1.7).

Answer: C

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