Does the line y = ax + b pass through the point (2, 5)?

Question

(1) When it is reflected around the x-axis, the line passes through the point (1 ,-6).

(2) When it is reflected around the y-axis, the line passes through the point (-3, 4).

GMATinsight · Accepted Answer

Question : Find the equation of line y = ax + b to find whether it passes through point (2, 5)?

Statement 1 :Reflection of line y = ax + b around the x-axis, passes through the point (1 ,-6).

There can be infinite Lines passing through (1, -6). Hence there can be infinite many reflections around x-axis and one of them will will pass through (2,5) and other will NOT
NOT SUFFICIENT

Statement 2 : Reflection of line y = ax + b around the y-axis, passes through the point (-3 ,4). 
There can be infinite Lines passing through (-3, 4). Hence there can be infinite many reflections around y-axis and one of them will will pass through (2,5) and other will NOT
NOT SUFFICIENT

Combining the two statements:  
Y axis Reflection of line passing through (-3, 4) will pass through (3, 4)
X axis Reflection of line passing through (1, -6) will pass through (1, 6)
There will be only one Line passing through these points and we can find out whether this line will have the point (2, 5) on it or not.. Hence
SUFFICIENT

Answer: option C

anudeep133 · Answer

Solution:  For (2,5) to pass through y = ax + b, 2a + b should be equal to 5.
If y = f(x) = ax + b , then
y = f(−x) is its reflection about the y-axis ==> y = -ax + b
y = −f(x) is its reflection about the x-axis ==> y = -ax - b

Statement1 : y = -ax - b passes through (1, -6) ==> -6 = -a - b ==> a + b = 6. Insufficient

Statement1 : y = -ax + b passes through (-3, 4) ==> 4 = 3a + b ==> 3a + b = 4. Insufficient

Combined : 2a = -2 ==> a = -1 and b = 7. It satisfies 2a + b = 5. So, yes. Sufficient.

Option C.

rohankant12 · Answer

Statement 1 tells you that 1 point is (1,6) - Insufficient
Statement 2 tells you that 1 point is (3,4) - Insufficient

Statement 1+2 - gives you 2 point. Thus, sufficient

Answer is C

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

Does the line y = ax + b pass through the point (2, 5)?

(1) When it is reflected around the x-axis, the line passes through the point (1 ,-6).

(2) When it is reflected around the y-axis, the line passes through the point (-3, 4).

In the original condition there are 2 variables for the line (the slope and the y-intercept, in other words a,b). We need 2 equations to match the number of variables and equations, and there is 1 each in 1) and 2) therefore C has high probability of being the answer. Using both 1) & 2) together, -y=ax+b passes through (1,-6) therefore 6=a+b. y=-ax+b passes through (-3,4) therefore 4=3a+b, and using both we can find the values of a and b. Therefore the answer is C

Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

yezz · Answer

the question asks whether the line passes through a certain point??

from 1

since the line reflections passes through (1,-6) then the line passes through (1,6), no idea about the slope ... endless possibilities ... insuff

from 2

since reflection passes through (-3,4) then the line passes through (3,4) , again endless possibilities ...insuff

using the 2 points we can get the slope and using ( slope and one point ) we can define one single line and thus determine whether the line passes through any given point ...suff

C

KrishnakumarKA1 · Answer

Solution:

To find:  The line y = ax + b through the point (2,5)?

Analysis of statement 1: When it is reflected around the x-axis, the line passes through the point (1 ,-6). 
Since the reflection given is with respect to the x-axis and passes through the point (1, -6), the line pass through the point (1,6). There can be an infinite number of possibilities that the line may pass through the point (2,5). 
Hence statement 1 is not sufficient to answer. We can eliminate options A and D.

Analysis of statement 2: When it is reflected around the y-axis, the line passes through the point (-3, 4). 
Since the reflection given is with respect to the y-axis and passes through the point (-3, 4), the line pass through the point (3,4). There can be an infinite number of possibilities that the line may pass through the point (2,5). 
Hence statement 2 is not sufficient to answer. We can eliminate options B.

Combining the statements 1 & 2 together: we get; 
From statements 1 and 2 we know that the line passes through the points (1,6) and (3,4). That means there will be one unique line which passes through these points and we can determine whether the point (2,5) will lie on the line or not. 
Hence combining the statements is sufficient to answer.

The correct answer option is “C”.

jrk23 · Answer

Anyone please explain me the equation of a line with Y axis as mirror. And when X axis is used as a mirror.

jainanant909 · Answer

I have a slight doubt. So, we know that the line y=ax+b passes through (1,6)   & (3,4)  . 
Now, to check whether y=ax+b passes through (2,5), do we need to find its slope? I mean how do we find out that the line passes through a point in such cases? 
I would have plugged in the values of (2,5) in y=ax+b but I do not have the value of b, which is the y-intercept. Please help me out.
I know there is no need to calculate for St 1&2 combined in this case, but I just want to understand the basics of it.

Does the line y = ax + b pass through the point (2, 5)?

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GMAT Data Sufficiency (DS) Questions

Does the line y = ax + b pass through the point (2, 5)?

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