Let f be a linear function with properties that f(1)< f(2) ,f (3)> f(4) and f(5)=5 ,which of the statement is true .

a) f(0)>8 b)f(0) =0 c) f(0)=5 d) f(0) =2 .

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- Md.Nazrul Islam
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The first condition states that f is an increasing function in the {1,2} range (thus the function will look like : y = mx + b)

The second condition states that f is a decreasing function in the {3,4} range. (thus the function will look like : y = -mx + b)

The two conditions are mutually exclusive for a linear function. (i.e. a linear function can only have one behaviour; either increasing or decreasing).

- sanju09
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Reasoning is a bit less than perfect, but yes, the question sounds dubious to me.Pharo wrote:Are you sure this is a valid question? I can see no way of drawing a linear function with these requirements. (This also does not fit in the "Data Sufficiency" type of questions)

The first condition states that f is an increasing function in the {1,2} range (thus the function will look like : y = mx + b)

The second condition states that f is a decreasing function in the {3,4} range. (thus the function will look like : y = -mx + b)

The two conditions are mutually exclusive for a linear function. (i.e. a linear function can only have one behaviour; either increasing or decreasing).

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Sanjeev K Saxena

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- Shalabh's Quants
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There looks to be mathematical fallacy in question...Pharo wrote:Are you sure this is a valid question? I can see no way of drawing a linear function with these requirements. (This also does not fit in the "Data Sufficiency" type of questions)

The first condition states that f is an increasing function in the {1,2} range (thus the function will look like : y = mx + b)

The second condition states that f is a decreasing function in the {3,4} range. (thus the function will look like : y = -mx + b)

The two conditions are mutually exclusive for a linear function. (i.e. a linear function can only have one behaviour; either increasing or decreasing).

Say linear fn is f(x)=ax+b;

Then, f(1)=a.1+b=a+b;

f(2)=a.2+b=2a+b;

As f(1)<f(2)...that means a+b < 2a+b => a>0;-----(1)

Again, f(3)=a.3+b=3a+b;

f(4)=a.4+b=4a+b;

As f(3)>f(4)...that means 3a+b > 4a+b => a<0;------(2)

Results from (1) & (2) are contradicting.

Shalabh Jain,

e-GMAT Instructor

e-GMAT Instructor

How would you make it perfect?sanju09 wrote:Reasoning is a bit less than perfect, but yes, the question sounds dubious to me.Pharo wrote:Are you sure this is a valid question? I can see no way of drawing a linear function with these requirements. (This also does not fit in the "Data Sufficiency" type of questions)

The first condition states that f is an increasing function in the {1,2} range (thus the function will look like : y = mx + b)

The second condition states that f is a decreasing function in the {3,4} range. (thus the function will look like : y = -mx + b)

The two conditions are mutually exclusive for a linear function. (i.e. a linear function can only have one behaviour; either increasing or decreasing).

- Shalabh's Quants
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Md.Nazrul Islam wrote:Let f be a linear function with properties that f(1)< f(2) ,f (3)> f(4) and f(5)=5 ,which of the statement is true .

a) f(0)>8 b)f(0) =0 c) f(0)=5 d) f(0) =2 .

There looks to be mathematical fallacy in question...

Say linear fn is f(x)=ax+b;

Then, f(1)=a.1+b=a+b;

f(2)=a.2+b=2a+b;

As f(1)<f(2)...that means a+b < 2a+b => a>0;-----(1)

Again, f(3)=a.3+b=3a+b;

f(4)=a.4+b=4a+b;

As f(3)>f(4)...that means 3a+b > 4a+b => a<0;------(2)

Results from (1) & (2) are contradicting.

Shalabh Jain,

e-GMAT Instructor

e-GMAT Instructor

This one got my attention

Firstly, the linear function can either increase or decrease, BUT it cannot increase and decrease at the same time. If the latter is a case, then we don't have a linear function.

The question explicitly states that f is a linear function, i.e. f(x)=ax+b where a is the slope and b is y-intercept. With the condition f(1)<f(2) the slope is positive (a>0). For f(3)>f(4), the slope is negative (a<0). Finally, with f(5)=5 the slope is unknown and we learn only about one point (x,y) as (5,5).

The answer choices given propose only one input of "

Because we are given not one but several functional relationships and our functions' y-intercepts are unknown, we may not answer this question. This is an example of the bad question-answer combination.

Firstly, the linear function can either increase or decrease, BUT it cannot increase and decrease at the same time. If the latter is a case, then we don't have a linear function.

The question explicitly states that f is a linear function, i.e. f(x)=ax+b where a is the slope and b is y-intercept. With the condition f(1)<f(2) the slope is positive (a>0). For f(3)>f(4), the slope is negative (a<0). Finally, with f(5)=5 the slope is unknown and we learn only about one point (x,y) as (5,5).

The answer choices given propose only one input of "

*x*" for f(x), this is x=0. So effectively, we may ignore our just recently "over-verbolized" theory of a function slope. We need only y-intercept to answet this question, because x=0. Is there any opportunity we can find the y-intercept from the data given in our question?Because we are given not one but several functional relationships and our functions' y-intercepts are unknown, we may not answer this question. This is an example of the bad question-answer combination.

Md.Nazrul Islam wrote:Let f be a linear function with properties that f(1)< f(2) ,f (3)> f(4) and f(5)=5 ,which of the statement is true .

a) f(0)>8 b)f(0) =0 c) f(0)=5 d) f(0) =2 .

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- Tommy Wallach
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Hey Guys,

Yep. Ignore questions like this. (It only has four answer choices!).

-t

Yep. Ignore questions like this. (It only has four answer choices!).

-t

Tommy Wallach, Company Expert

ManhattanGMAT

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