If ab#0 and a # -3b, what is the value of (4a + 6b)/(a + 3b)

Question

Tough and Tricky questions: Algebra.

If  ab 
eq 0  and  a 
eq -3b , what is the value of  \frac{(4a + 6b)}{(a + 3b)} ?

(1)  a - 3b = 6

(2)  \frac{2a}{(a + 3b)} = 4

Kudos for a correct  solution .

akumar5 · Answer

Expression given (4a+6b)/(a+3b)

This can be further reduced to 2(2a+3b)/(a+3b)
 2(a/(a+3b) +1)

statement 1 : a-3b=6 does not help us to get the value for the expression

statement 2: 2a/(a+3b) is self sufficient to get a definite value for the expression.

Answer is B

AliciaSierra · Answer

Given expression is \frac{(4a+6b)}{(a+3b)} .

Let us reduce this expression.

\frac{(2a+2a+6b)}{(a+3b)}

\frac{(2a+2*(a+3b))}{(a+3b)}

\frac{2a}{(a+3b)}   +   \frac{2*(a+3b)}{(a+3b)}

\frac{2a}{(a+3b)}   +  2 --- we have to find out value of this expression.

Statement 1. a-3b = 6 . Not suffcient

Statement 2. \frac{2a}{(a+3b)}  = 4. Let us put this value into question expression.

we will get 4+2 = 6

statement 2 is sufficient.

Answer: B

Regards,
Ammu

Bunuel · Answer

Official Solution:

If  ab 
eq 0  and  a 
eq -3b , what is the value of  \frac{(4a + 6b)}{(a + 3b)} ? 
 
We cannot simplify the given expression very much, because the denominator (which is a sum,  a + 3b ) is not a factor of the numerator. If we really wanted to, we could split the numerator and write the expression as a sum:
 
 \frac{4a}{(a + 3b)} + \frac{6b}{(a + 3b)} =  ?
 
Or we could leave the question as is. Either way, be sure not to cancel any of the coefficients, because the denominator is a sum - we can’t simply cancel the 6 in the numerator with the 3 in the denominator, for instance.
 
Statement 1: INSUFFICIENT. This gives us a relationship between  a  and  b . However, if we use it to solve for one of the variables and then we substitute that expression into the question, we'll quickly see that we will not get a single number:
 
From the statement:  a = 6 + 3b .
 
Substitute into the original question:
 
 \frac{4(6 + 3b) + 3b}{6 + 3b + 3b} =  ?
 
We can stop here if we see that the denominator is  6 + 6b , which will not cancel with the numerator of the combined fraction (which equals  24 + 15b ).
 
Statement 2: SUFFICIENT. We can get a constant ratio between  a  and  b , which will actually cancel in the question.
 
From the statement:
  \frac{2a}{(a + 3b)} = 4 
  2a = 4a + 12b 
  -2a = 12b 
  a = -6b 
 
Substitute into the question:
  \frac{4(-6b) + 6b}{-6b + 3b} = 
  = \frac{-24b + 6b}{-3b} 
  = \frac{-18b}{-3b} 
  = 6 
 
Note that it is okay to cancel out the  b 's, since  ab 
eq 0  and thus neither variable equals 0.
 
As long as we have a constant ratio between  a  and  b , we will get a number out of an expression such as  \frac{4a + 6b}{a + 3b} .
 
Answer: B.

mridupawandas · Answer

solving statement 2 we get a=-6b and then we substitute a =-6b in the given equation and we get -18/-3=6. hence B.

Lowkya · Answer

From Statement 1, 
It is given that a−3b=6.
Though we make a in terms of b or b in terms of a , still we will be left in 1 variable and not a value.
 So, Statement 1 is insufficient.

From Statement 2, 
 \frac{2a}{(a + 3b)} = 4 
 (a + 3b ) =\frac{a}{2}. 
Substitute this back in given fraction.
 \frac{( 2a + (2a + 6b) )}{(a + 3b )} 
 \frac{2a}{(a + 3b)} + \frac{2(a + 3b)}{(a + 3b)} 
=6.
 So, Statement 2 is sufficient.

Correct choice: B

DanTheGMATMan · Answer

Simplify the stem like this:

\frac{2a + (a+3b) + (a +3b)}{(a +3b)}

split the numerators and simplify so all you're left with is  \frac{2a}{(a+3b)}  + 1 + 1

All we need to know is the value of  \frac{2a}{(a+3b)} , condition B give us the value.

bumpbot · Answer

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If ab#0 and a # -3b, what is the value of (4a + 6b)/(a + 3b)

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If ab#0 and a # -3b, what is the value of (4a + 6b)/(a + 3b)

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