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# For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3

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Senior Manager
Joined: 25 Dec 2018
Posts: 488
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3  [#permalink]

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05 Mar 2019, 08:07
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25% (medium)

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79% (01:47) correct 21% (01:30) wrong based on 14 sessions

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For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3p−1, and 2p+1 equal to 12?

A) 2
B) 4
C) 5
D) 6
E) 8
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Joined: 12 Sep 2015
Posts: 4019
Re: For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3  [#permalink]

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05 Mar 2019, 08:19
Top Contributor
mangamma wrote:
For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3p−1, and 2p+1 equal to 12?

A) 2
B) 4
C) 5
D) 6
E) 8

If we take each answer choice and plug it into the given expressions (4p−1, 2p, 4p−12, 3p−1, and 2p+1), we see that most of them do not yield ANY values of 12.
For example, if p = 2, the expressions become: 4(2)−1, 2(2), 4(2)−12, 3(2)−1, and 2(2)+1
The expressions evaluate to be: 7, 4, -4, 5 and 5 {no 12's at all}

If p = 4, the expressions become: 4(4)−1, 2(4), 4(4)−12, 3(4)−1, and 2(4)+1
The expressions evaluate to be: 15, 8, 4, 11 and 9 {no 12's at all}

If p = 5, the expressions become: 4(5)−1, 2(5), 4(5)−12, 3(5)−1, and 2(5)+1
The expressions evaluate to be: 19, 10, 8, 14 and 11 {no 12's at all}

If p = 6, the expressions become: 4(6)−1, 2(6), 4(6)−12, 3(6)−1, and 2(6)+1
The expressions evaluate to be: 23, 12, 12, 17 and 13
AHA!! The mode here is 12

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Senior Manager
Joined: 25 Dec 2018
Posts: 488
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Re: For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3  [#permalink]

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05 Mar 2019, 08:20
GMATPrepNow wrote:
mangamma wrote:
For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3p−1, and 2p+1 equal to 12?

A) 2
B) 4
C) 5
D) 6
E) 8

If we take each answer choice and plug it into the given expressions (4p−1, 2p, 4p−12, 3p−1, and 2p+1), we see that most of them do not yield ANY values of 12.
For example, if p = 2, the expressions become: 4(2)−1, 2(2), 4(2)−12, 3(2)−1, and 2(2)+1
The expressions evaluate to be: 7, 4, -4, 5 and 5 {no 12's at all}

If p = 4, the expressions become: 4(4)−1, 2(4), 4(4)−12, 3(4)−1, and 2(4)+1
The expressions evaluate to be: 15, 8, 4, 11 and 9 {no 12's at all}

If p = 5, the expressions become: 4(5)−1, 2(5), 4(5)−12, 3(5)−1, and 2(5)+1
The expressions evaluate to be: 19, 10, 8, 14 and 11 {no 12's at all}

If p = 6, the expressions become: 4(6)−1, 2(6), 4(6)−12, 3(6)−1, and 2(6)+1
The expressions evaluate to be: 23, 12, 12, 17 and 13
AHA!! The mode here is 12

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For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3  [#permalink]

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05 Mar 2019, 21:30
mangamma wrote:
For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3p−1, and 2p+1 equal to 12?

A) 2
B) 4
C) 5
D) 6
E) 8

Mode:- The mode refers to the most frequently occurring number found in a set of numbers. If no elements in a set are repeated then mode doesn't exist for the set.

Here, mode=12(Given), which implies that there exists repetition of a number. Also, 'p' has to be integer.

Now equate the elements in variable form.

i.e, 1) 4p-1=2p; p=integer
2) 2p=4p-12 or 2p=12 or p=6

Ans. (D)
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For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3   [#permalink] 05 Mar 2019, 21:30
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