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

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Founder
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For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]  12 Aug 2018, 09:48
Expert's post
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Question Stats:

55% (00:44) correct 44% (01:13) wrong based on 52 sessions
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
[Reveal] Spoiler: OA

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Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]  13 Aug 2018, 06:32
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Least value of p = -4 -> |p| = 4

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

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

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Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]  16 Aug 2018, 14:38
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Why is the greatest value for p 4 and not 5?

Thank you
Founder
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Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]  17 Aug 2018, 05:06
Expert's post
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
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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.
Founder
Joined: 18 Apr 2015
Posts: 6562
Followers: 107

Kudos [?]: 1253 [1] , given: 5955

Re: For all values of the integer p such that 1.9 < |p| < 5.3 [#permalink]  01 Sep 2018, 10:17
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Expert's post
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
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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.

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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
Re: For all values of the integer p such that 1.9 < |p| < 5.3   [#permalink] 10 Sep 2018, 09:43
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