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# If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)

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If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)  [#permalink]

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Updated on: 31 Mar 2020, 01:24
2
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Difficulty:

55% (hard)

Question Stats:

61% (01:58) correct 39% (01:50) wrong based on 36 sessions

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If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)?

(A) -5
(B) -3
(C) 1
(D) 3
(E) 5

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Originally posted by GMATinsight on 31 Mar 2020, 00:23.
Last edited by GMATinsight on 31 Mar 2020, 01:24, edited 3 times in total.
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If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)  [#permalink]

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Updated on: 31 Mar 2020, 01:25
at f(1) ; 2f(-1)+3f(1) = -15---(a)
and at f(-1) ; 2(f1)+3f(-1)=-5---(b)
we get
5f(1)+5f(-1) = -20
f(1)+f(-1) = -4
f(1)= -4-f(-1)
substitute value of f(1) in (a)
we get
2f(-1)-12-3f(-1)=-15
solve for f(-1) ; = + 3
Option D is correct

Originally posted by Archit3110 on 31 Mar 2020, 00:35.
Last edited by Archit3110 on 31 Mar 2020, 01:25, edited 2 times in total.
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Re: If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)  [#permalink]

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31 Mar 2020, 00:46
This is very good question based on function:

2f(x) + 3f(-x) = 5x − 10

Putting x=1, 2f(1) + 3f(-1) = 5*1-10 = -5... eq(1)

Putting x=-1, 2f(-1) + 3f(1) = 5*(-1) − 10 = -15... eq(2)

Multiply equation 1 with 3 and equation 2 with 2 and subtract

5*f(-1) = -5*3- (-15*2) = 15

f(-1) = 15/5 = 3

GMATinsight wrote:
If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)?

(A) -5/8
(B) 8/5
(C) -8/5
(D) 3/5
(E) -3/5

2f(x) + 3f(-x) = 2x − 7

@x=1, 2f(1) + 3f(-1) = 2 − 7 = -5

@x=-1, 2f(-1) + 3f(1) = -2 − 7 = -9

Multiply equation 1 with 3 and equation 2 with 2 and subtract

5*f(-1) = -15+18 = 3

f(-1) = 3/5

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If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)  [#permalink]

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Updated on: 31 Mar 2020, 01:25
archit
GMATBusters

I am so sorry, I meant to give function value as 2x-7 but by mistake I wrote it as 5x-10

Now, I am keeping it the same and making amendment in option values
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Originally posted by GMATinsight on 31 Mar 2020, 01:20.
Last edited by GMATinsight on 31 Mar 2020, 01:25, edited 1 time in total.
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Re: If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)  [#permalink]

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31 Mar 2020, 01:25
1
GMATinsight wrote:
If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)?

(A) -5
(B) -3
(C) 1
(D) 3
(E) 5

The detailed solution is as mentioned below

Attachments

Screenshot 2020-03-31 at 2.53.53 PM.png [ 743.27 KiB | Viewed 432 times ]

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Re: If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)  [#permalink]

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08 Apr 2020, 03:38
GMATinsight wrote:
If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)?

(A) -5
(B) -3
(C) 1
(D) 3
(E) 5

for x=-1
2f(-1) + 3f(-(-1)) =5(-1) -10 => -15
=> 3f(1) + 2f(-1) = -15 ........... (1)

For x=1
2f(1) + 3f(-(1)) =5(1) -10
-> 2f(1)+ 3f(-1) = -5............(2)

For ease, consider f(1) = m and f(-1) = n
=>in (1) we have,
3m + 2n = -15.......(A)
=> in (2) we have,
2m + 3n = -5 ......(B)

Two eq with 2 variables, Solve (A) and (B) for 'n'

we have n=3 => f(-1) =3

IMO- D
Re: If 2f(x) + 3f(-x) = 5x − 10, what is the value of f(-1)? (A) -5/8 (B)   [#permalink] 08 Apr 2020, 03:38