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Which of the following could be p if |3p – 4| < 1?

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Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 25 Dec 2016, 02:35
3
2
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A
B
C
D
E

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  15% (low)

Question Stats:

77% (01:03) correct 23% (01:10) wrong based on 329 sessions

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Re: Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 25 Dec 2016, 02:45
1
|3p-4| <1
=-1< 3p-4 <1
= 3<3p<5
= 1< P<5/3

So ans is (B) which satisfies the above equation

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Re: Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 15 Jan 2018, 09:48
Bunuel wrote:
Which of the following could be p if |3p – 4| < 1?

A. 1/4
B. 5/4
C. 5/3
D. 0
E. 2

No need to solve this question , just plug in and check ( 10 sec) answer will definitely be (B)

\(\frac{3*5}{4} - 4\)

= \(\frac{1}{4}\), answer will be clearly (B)

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Re: Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 05 Mar 2018, 09:37
Can someone please, explain my mistake:

Which of the following could be p if |3p – 4| < 1?

A. 1/4 B. 5/4 C. 5/3 D. 0 E. 2

a. |3p – 4| < 1; 3p < 1 + 4; p <5/3

b. |3p – 4| < 1; 3p <-1 + 4; p < 3/3; p < 1

I selected 1/4, being more restricitive.
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Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 05 Mar 2018, 21:13
hero_with_1000_faces wrote:
Can someone please, explain my mistake:

Which of the following could be p if |3p – 4| < 1?

A. 1/4 B. 5/4 C. 5/3 D. 0 E. 2

a. |3p – 4| < 1; 3p < 1 + 4; p <5/3

b. |3p – 4| < 1; 3p <-1 + 4; p < 3/3; p < 1

I selected 1/4, being more restricitive.

Highlighted part is incorrect.

If you open brackets with a < sign. . .

Case 1: absolute value < RHS
3P - 4 < 1
3P < 5
P < \(\frac{5}{3}\)

Case 2: absolute value > -RHS
3P - 4 > -1
3P > 3
P > 1

and
P < \(\frac{5}{3}\)

1 < P < \(\frac{5}{3}\)

P has to fall between 1 and \(\frac{5}{3}\)

Only \(\frac{5}{4}\) does that.

0 and \(\frac{1}{4}\) are too small.

\(\frac{5}{3}\) and 2 are too great.

Easy mistake to make in the arithmetic. :-) Hope that helps
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Re: Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 05 Mar 2018, 23:33
generis Thank you for your kind explanation. I have read Manhattan, gone through magoosh videos and still had a flawed understanding. Thank You.




generis wrote:
hero_with_1000_faces wrote:
Can someone please, explain my mistake:

Which of the following could be p if |3p – 4| < 1?

A. 1/4 B. 5/4 C. 5/3 D. 0 E. 2

a. |3p – 4| < 1; 3p < 1 + 4; p <5/3

b. |3p – 4| < 1; 3p <-1 + 4; p < 3/3; p < 1

I selected 1/4, being more restricitive.

Highlighted part is incorrect.

If you open brackets with a < sign. . .

Case 1: absolute value < RHS
3P - 4 < 1
3P < 5
P < \(\frac{5}{3}\)

Case 2: absolute value > -RHS
3P - 4 > -1
3P > 3
P > 1

and
P < \(\frac{5}{3}\)

1 < P < \(\frac{5}{3}\)

P has to fall between 1 and \(\frac{5}{3}\)

Only \(\frac{5}{4}\) does that.

0 and \(\frac{1}{4}\) are too small.

\(\frac{5}{3}\) and 2 are too great.

Easy mistake to make in the arithmetic. :-) Hope that helps
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Re: Which of the following could be p if |3p – 4| < 1?  [#permalink]

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New post 08 Mar 2018, 11:39
Bunuel wrote:
Which of the following could be p if |3p – 4| < 1?

A. 1/4
B. 5/4
C. 5/3
D. 0
E. 2


Scanning our answer choices, we see that answer choice B is correct.

|3(5/4) - 4| < 1

|15/4 - 4| < 1

|15/4 - 16/4| < 1

|-1/4| < 1

1/4 < 1

Alternate Solution:

In order for the absolute value of an expression to be less than 1, the value of the expression itself must be between -1 and 1; in other words, we must have:

-1 < 3p - 4 < 1

3 < 3p < 5

1 < p < 5/3

5/4 is the only value amongst the answer choices that is included in this interval.

Answer: B
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Re: Which of the following could be p if |3p – 4| < 1?   [#permalink] 08 Mar 2018, 11:39
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