15a + 6b = 30, what is the value of a - b ?

Question

Competition Mode Question

15a + 6b = 30 , what is the value of  a - b  ?

(1)  b = 5 – 2.5a 
(2)  9b = 9a – 81

freedom128 · Answer

Eq (1) 15a + 6b =30

1. 2.5a + b = 5 
--> 15a + 6b = 30
This is the same with Eq (1). We then cannot determine the value of a, b and a-b. 
NOT SUFFICIENT.

2. 81=9a-9b
-->9=a-b
We then can determine the value of a-b. 
SUFFICIENT.

FINAL ANSWER IS (B)

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lacktutor · Answer

If 15a + 6b= 30, what is the value of a —b= ?

(Statement1): b= 5 —2.5a
—> 6*b= 6*(5–2.5a) 
6*b = 30 —15a 
—> 15a + 6b= 30 
a—b could be anything 
Insufficient

(Statement2): 9b= 9a —81 
—> 9(a—b) = 81 
a—b = 9 
Sufficient

The answer is B

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eakabuah · Answer

Given that 15a+6b=30, we are to determine b-a
15a+6b=30........(1)
Statement 1: b=5-2.5b
multiplying 1 by 6, we have 6b=30-15a
Hence 15a+6b=30......(2) 
Statement 1 is insufficient because (2) is identical to (1).

Statement 2: 9b=9a-81
9b-9a=-81, which can be reduced to b-a=-9............(3)
solving (1) and (2) yields a=4; and b=-5
hence b-a=-9.
Statement 2 alone is sufficient

The answer is B.

kiekiis · Answer

15a + 6b = 30, what is the value of a - b ?

(1) b=5–2.5a
Substitute b in to the equation and we will be able to get 
15a+6(5–2.5a)=30
15a+30-15a=30
Will see that a is unable to find, so  statement 1 is insufficient .

(2) 9b=9a–81
From statement 2, b=a-9
Substitute b in the equation will get:
15a+6(a-9)=30
15a+6a-54=30
21a=84
a=4
Substitute b in the equation will get:
15(4)+6b=30
60+6b=30
6b=-30
b=-5

Since a and b can be solved,  statement 2 is sufficient .
Therefore  B .

Archit3110 · Answer

given
5a+2b=10
or say b=5-2.5a
#1
b=5–2.5a
no info insufficeint
#2
9b=9a–81
b=a-9
so a-b= 9
sufficient
IMO B

15a+6b=30, what is the value of a−b ?

(1) b=5–2.5a
(2) 9b=9a–81

unraveled · Answer

15a+6b=30, what is the value of a−b ?
5a + 2b = 10

(1) b=5–2.5a
Solving,
5a + 2b = 10 nothing new.

INSUFFICIENT.

(2) 9b=9a–81
9a - 9b = 81
a - b = 9

SUFFICIENT.

Answer B.

exc4libur · Answer

(1) b=5–2.5a   insufic

15a+6b=30
5a+2b=10
b=5-2.5a (same info as in statement 1)

(2) 9b=9a–81   sufic

9b=9a-81
b=a-9
a-9=5-2.5a
3.5a=14
a=4

Ans (B)

madgmat2019 · Answer

(1) b=5–2.5a............its the simplified form of the given equation.....so no use.....INSUFFICIENT
(2) 9b=9a–81........ans:9....SUFFICIENT

OA:B

Bunuel · Answer

OFFICIAL EXPLANATION

Be aware that simply because you have two equations with two unknowns does not mean that a solution exists. You must have two unique equations with two unknowns in order for a solution to exist.

Evaluate Statement (1) alone.

There are two possible ways to solve this problem:
Method (1): Substitute b from Statement (1) into the original equation.
15a + 6(5 – 2.5a) = 30
15a + 30 - 15a = 30
30 = 30
0 = 0
Based upon this answer, the equation in Statement (1) is the equation in the original question solved for b. Consequently, we only have one equation and two unknowns. There is not enough information to determine a-b.

Method (2): Rearrange the equation in Statement (1) and subtract this equation from the original equation.
b = 5 – 2.5a
b + 2.5a = 5
2.5a + b = 5
Multiply by 6 so b's cancel:15a + 6b = 30
This method also shows that the equation in Statement (1) is nothing more than the original equation rearranged. Consequently, we only have one equation and two unknowns. There is not enough information to determine a-b.
Statement (1) is NOT SUFFICIENT.

Evaluate Statement (2) alone.

Try to line up the two equations so that you can subtract them:
9b = 9a – 81
81 + 9b = 9a
81 = 9a - 9b
Statement (2) Equation: 9a - 9b = 81
Original Question Equation: 15a + 6b = 30
At this point, you can stop since you know that you have two unique equations and two unknowns. Consequently, there will be a solution for a and for b, which means there will be one unique value for a-b. Statement (2) is SUFFICIENT.

If you want to solve to see this (Note: Do not solve this in a test as it takes too much time and is not necessary):
Multiply (2) by 4: 36a - 36b = 324
Multiply Original by 6: 90a + 36b = 180

6*Original + 2*Statement(2): (90a + 36a) + (36b + -36b) = 180 + 324
126a = 204
a = 4

Solve for b:
9b = 9(4) - 81 = -45
b = -5

a - b = 4 - (-5) = 4 + 5 = 9

Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.

AkshadSoman · Answer

Hey there, if anyone can answer the following question I have! 
If I get the value of “ a” and “b” individually I can get the value of “a-b” so by this logic option “d” should be correct since I can get the values of both variables by either equation.

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15a + 6b = 30, what is the value of a - b ?

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GMAT Data Sufficiency (DS) Questions

15a + 6b = 30, what is the value of a - b ?

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