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If 3a – 2b – 2c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?

A) 3 B) 9 C) 10 D) 12 E) 14

Hi, when we look at the two equations, we can relize some similarity, so lets work on it.. 3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32 {√3a-√(2b+2c)}{√3a+√(2b+2c)}=32.. or 4*√3a+√(2b+2c)=32.. or √3a+√(2b+2c)=8..

now lets work on these two equations 1)√3a-√(2b+2c)=4.. 2)√3a+√(2b+2c)=8..

A) add the two eq.. √3a+√(2b+2c)+√3a-√(2b+2c)=12.. 2√3a=12.. or √3a=6.. 3a=36.. a=12.

B) subtract 1 from 2.. √3a+√(2b+2c)-√3a+√(2b+2c)=4.. 2√(2b+2c)=4.. √(2b+2c)=2.. 2b+2c=4.. or b+c=2..

from A and B a+b+c=12+2=14.. E Hope it helped
_________________

Re: If 3a – 2b – 2c = 32 and 3a - 2b + 2c = 4, what is the value of a + b [#permalink]

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02 Oct 2017, 11:44

Bunuel wrote:

If 3a – 2b – 2c = 32 and \(\sqrt{3a}- \sqrt{2b + 2c} = 4\), what is the value of a + b + c ?

A. 3 B. 9 C. 10 D. 12 E. 14

I will use plugging in . Given the equations and the options, a is likely 12 and a+b+c is 14. For further checking, 2b+2c = 4 and \sqrt{2b + 2c} = 2, making a=b=1. Hence, a+b+c = 12+2(1) = 14.

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: If 3a – 2b – 2c = 32 and 3a - 2b + 2c = 4, what is the value of a + b [#permalink]

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02 Oct 2017, 12:07

rulingbear wrote:

Bunuel wrote:

If 3a – 2b – 2c = 32 and \(\sqrt{3a}- \sqrt{2b + 2c} = 4\), what is the value of a + b + c ?

A. 3 B. 9 C. 10 D. 12 E. 14

I will use plugging in . Given the equations and the options, a is likely 12 and a+b+c is 14. For further checking, 2b+2c = 4 and \sqrt{2b + 2c} = 2, making a=b=1. Hence, a+b+c = 12+2(1) = 14.

I don't think plugging in is a good idea for this question.... How did u directly arrived at a = 12 ??
_________________

If 3a – 2b – 2c = 32 and 3a - 2b + 2c = 4, what is the value of a + b [#permalink]

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02 Oct 2017, 12:19

1

This post received KUDOS

shashankism wrote:

rulingbear wrote:

Bunuel wrote:

If 3a – 2b – 2c = 32 and \(\sqrt{3a}- \sqrt{2b + 2c} = 4\), what is the value of a + b + c ?

A. 3 B. 9 C. 10 D. 12 E. 14

I will use plugging in . Given the equations and the options, a is likely 12 and a+b+c is 14. For further checking, 2b+2c = 4 and \sqrt{2b + 2c} = 2, making a=b=1. Hence, a+b+c = 12+2(1) = 14.

I don't think plugging in is a good idea for this question.... How did u directly arrived at a = 12 ??

Good question. It needs keen observation

1. From the first equation, 3a is likely to be greater than 32 2. From the second equation, [m]\sqrt{3a} is likely to be greater than 4

Put this inference together and a could be 12, i.e 3*12= 36>32, and \sqrt{3*12} = 6>4

The same could be used to know that a= b= 1, as explained in my earlier post. Even without doing this you should know by now that the answer is E.

This is a good must be true type of question, it could also make a decent data sufficiency question. Just observing keenly will obviously save a lot of time!

Another way to look at it is the form of the equation, take the first equation, 3a - 2a- 2b= 32. This can be rearranged as 3a - 2(a+b)= 32, therefore a must be an even number and a+b will also be even. Given this, a+b+c would be an even number of the x+2y. Only 10,12 and 14 are viable. Looking at the second equation will tell you that x/a would be 12 as 3a would form the only proper square.

Last edited by rulingbear on 02 Oct 2017, 12:50, edited 1 time in total.

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

If 3a – 2b – 2c = 32 and 3a - 2b + 2c = 4, what is the value of a + b [#permalink]

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02 Oct 2017, 12:30

rulingbear wrote:

Good question. It needs keen observation

1. From the first equation, 3a is likely to be greater than 32 2. From the second equation, [m]\sqrt{3a} is likely to be greater than 4

Put this inference together and a could be 12, i.e 3*12= 36>32, and \sqrt{3*12} = 6>4

The same could be used to know that a= b= 1, as explained in my earlier post. Even without doing this you should know by now that the answer is E.

This is a good must be true type of question, it could also make a decent data sufficiency question. Just observing keenly will obviously save a lot of time!

3a>32 already includes [m]\sqrt{3a} is be greater than 4. So we should further work on 3a>32..

But your observation is appreciable and surely can be used here to solve the problem using plugging method..
_________________

Re: If 3a – 2b – 2c = 32 and 3a - 2b + 2c = 4, what is the value of a + b [#permalink]

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02 Oct 2017, 12:55

shashankism wrote:

rulingbear wrote:

Good question. It needs keen observation

1. From the first equation, 3a is likely to be greater than 32 2. From the second equation, [m]\sqrt{3a} is likely to be greater than 4

Put this inference together and a could be 12, i.e 3*12= 36>32, and \sqrt{3*12} = 6>4

The same could be used to know that a= b= 1, as explained in my earlier post. Even without doing this you should know by now that the answer is E.

This is a good must be true type of question, it could also make a decent data sufficiency question. Just observing keenly will obviously save a lot of time!

3a>32 already includes [m]\sqrt{3a} is be greater than 4. So we should further work on 3a>32..

But your observation is appreciable and surely can be used here to solve the problem using plugging method..

There is no need to actually work further once you know 3a>32, a is most likely 12 and the answer can only be 14, given the options.