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If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

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by BTGModeratorVI » Tue Mar 03, 2020 6:47 am

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If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

A. 6
B. 8
C. 10
D. 12
E. It cannot be determined from the information given.

Answer: C
Source: Princeton Review
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Re: If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

by Jay@ManhattanReview » Tue Mar 03, 2020 10:06 pm
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:47 am
 If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

A. 6
B. 8
C. 10
D. 12
E. It cannot be determined from the information given.

Answer: C
Source: Princeton Review
From 4r + 3s = 7 and 2r + s = 1, we get r = –2 and s = 5.

From 2r + 2s = t – 4, we get t = 2(r + s) + 4

Thus, t = 2(r + s) + 4 = 2(–2 + 5) + 4 = 10.

The correct answer: C

Hope this helps!

-Jay
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Re: If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

by Brent@GMATPrepNow » Mon Mar 09, 2020 6:12 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:47 am
 If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

A. 6
B. 8
C. 10
D. 12
E. It cannot be determined from the information given.

Answer: C
Source: Princeton Review
GIVEN:
4r + 3s = 7
2r + s = 1
2r + 2s = t – 4


Take:
4r + 3s = 7
2r + s = 1
Subtract bottom equation from top equation to get: 2r + 2s = 6

Now take:
2r + 2s = t – 4
2r + 2s = 6
Subtract bottom equation from top equation to get: 0 = t - 10
If t - 10 = 0, then t = 10

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

by Scott@TargetTestPrep » Wed Mar 11, 2020 9:40 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:47 am
 If 4r+3s=7, 2r+s=1, and 2r+2s=t–4, what is the value of t?

A. 6
B. 8
C. 10
D. 12
E. It cannot be determined from the information given.

Answer: C
Source: Princeton Review
If we subtract the second equation from the first, we have 2r + 2s = 6. Since 2r + 2s = t - 4, then we must have 6 = t - 4. Therefore, t = 10.

Answer: C

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