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?
Which of the following could be t if |5t – 8| < 1?
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- EconomistGMATTutor
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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.
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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- Scott@TargetTestPrep
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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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