What number is 6 more than x + y ? (1) y is 3 less than x. (2) y is t

We need to determine 6 + x + y.

Statement One Alone:

y = x - 3

We do not have enough information to determine x, y or x + y. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

y is twice x.

Once again, we do not have enough information to determine x, y or x + y. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using substitution, we have:

2x = x - 3

x = -3, so y = -6, and hence x + y + 6 = -3.

Answer: C
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We're asked to calculate x + y + 6 so we need to know x + y.
We'll look for the relevant information, a Logical approach.

(1) gives y = x - 3, not what we need. Insufficient.
(2) gives y = 2x, still not what we need. Insufficient.
Together is 2 equations with 2 variables, sufficient to calculate both x and y so enough to calculate x+y.
(C) is our answer.

#1
y=x-3
y+x ; 2x-3 ; x= 3/2
insufficeint
#2
y=2x
3x from x+y
insufficient
from 1 &2
we know
2x=x-3
x=-3 so -3+6 ; 3
IMO C sufficient

The original question: \(x+y+6=?\)
The rephrased question: \(x+y=?\)

1) We know that \(y=x-3\) and can use the statement information to further rephrase the question.

\(x+x-3=?\)

Since \(x\) can be any real number, we can't get a unique value to answer the further rephrased question. \(\implies\) Insufficient

2) We know that \(y=2x\) and can use the statement information to further rephrase the question.

\(x+2x=?\)

Since \(x\) can be any real number, we can't get a unique value to answer the further rephrased question. \(\implies\) Insufficient

1&2) The system of equations \(y=x-3\) and \(y=2x\) has a unique solution. Thus, we could get a unique value to answer the rephrased question. \(\implies\) Sufficient

Answer: C

Target question: What is the value of x + y + 6?

Statement 1: y is 3 less than x.
We can write: y = x - 3
There are several values of x and y that satisfy this equation. Here are two:
Case a: x = 3 and y = 0. In this case, the answer to the target question is x + y + 6 = 3 + 0 + 6 = 9
Case b: x = 4 and y = 1. In this case, the answer to the target question is x + y + 6 = 4 + 1 + 6 = 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is twice x.
We can write: y = 2x
There are several values of x and y that satisfy this equation. Here are two:
Case a: x = 1 and y = 2. In this case, the answer to the target question is x + y + 6 = 1 + 2 + 6 = 9
Case b: x = 2 and y = 4. In this case, the answer to the target question is x + y + 6 = 2 + 4 + 6 = 12
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y = x - 3
Statement 2 tells us that y = 2x
We have 2 DIFFERENT linear equations with 2 variables.
Since we COULD solve the system for x and y, we COULD determine the value of x + y + 6
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.

Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Hi All,

We're asked what number is 6 MORE than (X+Y). This question can be approached in a couple of different ways, including by TESTing VALUES. It's worth noting that the prompt does NOT place any restrictions on X and Y, so they could be positive, negative, 0, fractions, etc.

(1) Y is 3 LESS than X.

IF....
X=3 and Y=0, then the answer to the question is 3+0+6 = 9
X=4 and Y=1, then the answer to the question is 4+1+6 = 11
Fact 1 is INSUFFICIENT

(2) Y is TWICE X.
IF....
X=1 and Y=2, then the answer to the question is 1+2+6 = 9
X=2 and Y=4, then the answer to the question is 2+4+6 = 12
Fact 2 is INSUFFICIENT

Combined, we know...
Y is 3 LESS than X.
Y is TWICE X.

At this point, you might wonder how Y is LESS than X while also being TWICE X. This can happen when the variables are NEGATIVE. We can create the following two equations with the given information:
Y = X - 3
Y = 2X

This is a 'System' of equations (2 variables and 2 unique equations), so we CAN solve for the exact values of X and Y. They are:
2X = X - 3
X = -3
Y = -3 - 3 = -6

Thus, the answer to the question is (-3)+(-6)+6 = -3
Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

essentially question is asking value of x+y+6=??
for that we need to calculate x+y=?

a) y=x-3 => x-y=3 (single equation with 2 variable) Not Sufficient (cancel A,D)
b)y=2x (single equation with 2 variable) Not Sufficient (cancel B)

Together a&b => 2 equation 2 variable: sufficient to find a&b, which will help to calculate x+y+6 (As required)
Sufficient (C)

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Answer: Option C

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I also got answer choice C.

However after reviewing my result I discovered that I had read the question wrong and am wondering how I can prevent misreading the question next time. To me it seems like the question is ambiguous if you were to solve the equations.

I got x = -3 & y = -6. The question asks: What number is 6 more than x + y ? Well x+y is -3 + (-6) = -9 hence I would have answered that the number that 6 is more than x+y is 15. (Because -9 +15 =6)

Only after reviewing the question did I realize that the question is actually asking what is x+y+6. But I still find it difficult to understand because it seems ambiguose to me.

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