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# If 3a + 2b – 4 = a – b, what is the value of b ?

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Current Student
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If 3a + 2b – 4 = a – b, what is the value of b ?  [#permalink]

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23 Jul 2014, 09:48
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25% (medium)

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75% (01:05) correct 25% (01:11) wrong based on 149 sessions

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If 3a + 2b – 4 = a – b, what is the value of b ?

(1) 2a^2 = 50

(2) 4a = 20

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Joined: 02 Sep 2009
Posts: 52152
Re: If 3a + 2b – 4 = a – b, what is the value of b ?  [#permalink]

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23 Jul 2014, 09:53
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If 3a + 2b – 4 = a – b, what is the value of b ?

3a + 2b – 4 = a – b --> 2a + 3b = 4.

(1) 2a^2 = 50 --> a^2 = 25 --> a = 5 or a = -5. We'll get two different values of b, when substituting these value into 2a + 3b = 4. Not sufficient.

(2) 4a = 20 --> a = 5. We can substitute into 2a + 3b = 4 and get the value of b. Sufficient.

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

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19 Jul 2016, 13:38
Simplifying question stem 3a + 2b – 4 = a – b , we get 2a + 3b = 4

Statement 1 is 2$$a^2$$ = 50
simplifying $$a^2$$ = 25 , we don't know whether a is positive or negative
a can be 5 or -5 so insufficient

Statement 2 is 4a = 20
clearly we get a = 5 so sufficient
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Re: If 3a + 2b – 4 = a – b, what is the value of b ?  [#permalink]

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19 Jul 2016, 16:32
Gnpth wrote:
If 3a + 2b – 4 = a – b, what is the value of b ?

(1) 2a^2 = 50

(2) 4a = 20

3a + 2b – 4 = a – b
2a+3b= 4

(1) 2a^2 = 50
'a' can be +5 or -5, and hence it will give different values for 'b'

Not Sufficient.

(2) 4a = 20
a= 5

Sufficient.

Putting the value of a in the equation gives the value of b.

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

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19 Sep 2016, 07:04
B is correct. Here's why:

(1) 2(a^2) = 50 --> a^2 = 25 --> a = +/- 5

INSUFFICIENT

(2) 4a = 20 --> a = 5

Plug into main equation --> 2(5) + 3b - 4 = 0 --> solve for b

SUFFICIENT
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Re: If 3a + 2b – 4 = a – b, what is the value of b ?  [#permalink]

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28 Dec 2017, 21:12
Given is 3a + 2b = a - b + 4
2a + 3b = 4. Now value of b is to be calculated
(1) Insufficient: a^2 = 25
a = 5 or -5. Hence, b will have 2 values.

(2) Sufficient: a = 5, hence b = -2.
Re: If 3a + 2b – 4 = a – b, what is the value of b ? &nbs [#permalink] 28 Dec 2017, 21:12
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