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For all values of the integer p such that 1.9 < |p| < 5.3

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Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 21056

For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

12 Aug 2018, 09:48

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For all values of the integer p such that \(1.9 < |p| < 5.3\), the function \(f(p) = p^2\) .

Quantity A	Quantity B
f(p) for the greatest value of p	f(p) for the least value of p

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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Romang67

Intern

Joined: 10 Aug 2018

Posts: 33

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

13 Aug 2018, 06:32

Least value of p = -4 -> |p| = 4

Greatest value of p = 4 -> |p| = 4

f(-4) = f(4) = 16

So the answer is C.

DiamondsAndHistones

Intern

Joined: 16 Aug 2018

Posts: 4

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

16 Aug 2018, 14:38

Why is the greatest value for p 4 and not 5?

Thank you

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 21056

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

17 Aug 2018, 05:06

Expert Reply

In fact, in the range the least and the greatest values are -5 and 5 for which \(f(p)=p^2\).

4 is wrong. incidentally, the answer is still C but the value considered in the range is wrong.

Regards

IshanGre

Manager

Joined: 29 Nov 2017

Posts: 190

Location: United States

GRE 1: Q142 V146

WE:Information Technology (Computer Software)

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

01 Sep 2018, 08:47

Carcass wrote:

In fact, in the range the least and the greatest values are -5 and 5 for which \(f(p)=p^2\).

4 is wrong. incidentally, the answer is still C but the value considered in the range is wrong.

Regards

how come -5 it is 1.9 < |p| < 5.3..please elaborate.

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 21056

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

01 Sep 2018, 10:17

Expert Reply

it is still -5 that into the absolute value becomes +5 and as it turns out: the least value is at the same time the GREATEST value in the range.

Hope this helps.

Regards

saifee

Intern

Joined: 10 Sep 2018

Posts: 20

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

10 Sep 2018, 09:35

from the inequality, and the properties of absolute values, we can say that p has two separate/disjoint ranges of values: (-5.3, -1.9) and (1.9, 5.3).

so the lowest and the highest values p can take are -5.3 and 5.3, both of which give the same result when plugged into the function.

so the answer is C.

shovon02

Intern

Joined: 10 Sep 2018

Posts: 1

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

10 Sep 2018, 09:43

Carcass wrote:

For all values of the integer p such that \(1.9 < |p| < 5.3\), the function \(f(p) = p^2\) .

Quantity A	Quantity B
f(p) for the greatest value of p	f(p) for the least value of p

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E

NickBass

Manager

Joined: 02 Mar 2020

Posts: 54

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

04 Mar 2020, 14:18

So basically because it's absolute value we must take the highest in the range as both a positive and a negative?

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 21056

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

04 Mar 2020, 16:15

Expert Reply

Yes. Basic rule

See the attachment for all the math concepts you do need

Attachment:

GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]
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bumpbot

CEO

Joined: 07 Jan 2021

Posts: 2698

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]

22 Apr 2021, 07:20

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