Simple Math problem

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AndyB: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sat Oct 16, 2010 9:31 pm

by AndyB » Sun Oct 09, 2011 3:38 am

Hello Everyone,

Anybody!!! Please help me in solving the below problem.

5) The relationship between x and y is given as:

x 0 1 2 3 4 5 6
y 0 10 40 90 160 250 360

If x=2.5, what will be the value of y??

a)45
b)62.5
c)65
d)67.5

I am not able to understand how to derive a relationship between x and y...and then use x=2.5 and then get the result of y.

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Source: Beat The GMAT — Problem Solving | Sun Oct 09, 2011 3:38 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Oct 09, 2011 3:49 am

AndyB wrote:The relationship between x and y is given as:

x 0 1 2 3 4 5 6
y 0 10 40 90 160 250 360

If x=2.5, what will be the value of y?

y is nothing but 10 multiplied with the square of x.

Hence, for x = 2.5, y = 10*(2.5)^2 = 62.5

The correct answer is B.

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GMAT Expert, Admissions and Career Guidance
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parul9: Master | Next Rank: 500 Posts; Posts: 197; Joined: Thu Sep 15, 2011 10:22 amFollowed by: 2 members; Thanked: 6 times

by parul9 » Sun Oct 09, 2011 4:45 am

B!
the relation is y = 10x^2
And then substitution of x = 2.5 gives y = 62.5

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Oct 09, 2011 5:59 am

AndyB wrote:Hello Everyone,

Anybody!!! Please help me in solving the below problem.

5) The relationship between x and y is given as:

x 0 1 2 3 4 5 6
y 0 10 40 90 160 250 360

If x=2.5, what will be the value of y??

a)45
b)62.5
c)65
d)67.5

I am not able to understand how to derive a relationship between x and y...and then use x=2.5 and then get the result of y.

0 = 0 * 10

10 = 1^2 * 10

40 = 2^2 * 10

90 = 3^2 * 10

160 = 4^2 * 10

250 = 5^2 * 10

360 = 6^2 * 10

So actually y = ( x^2 ) *10

hence when x = 2.5

Y = 2.5^2 * 10

y =>6.25

Abhishek

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GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Sun Oct 09, 2011 7:02 am

AndyB wrote: 5) The relationship between x and y is given as:

x 0 1 2 3 4 5 6
y 0 10 40 90 160 250 360

If x=2.5, what will be the value of y?

The best thing here is just to be so familiar with the sequence of the first few perfect squares, that the relationship just jumps out at you. But what if it doesn't?

If you absolutely cannot see what the formula should be just by looking at it, you can use the following:

Write down the differences between successive y-values, and then write down the differences between those first differences:

y= 0 10 40 90 160 250 360
differences= 10,30,50,70,90,110.
2nd diff= 20,20,20,20,20,20

There is a rule that says if the second differences of a sequence are constant(in this case 20), then the sequence can be modeled by a quadratic equation(that is y=ax^2+bx+c). This would tell you that the formula definitely involves x^2, and hopefully you would be able to see the relationship from there. If you still can't, proceed as follows:

We know the formula is of the form y=ax^2+bx+c and that y=0 when x=0, so plug in these values:
0=a*0^2+b*0+c
0=c

we know c is zero, so it must be that y=ax^2+bx. Now plug in another set of values, x=1, y=10

10=a+b

and another set of values: x=2 y=40

40=4a+2b

Solving this system of equations gives a=10, b=0 so the model is y=10x^2.

But again, this should be a last resort because of the time involved.

Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial

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AndyB: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sat Oct 16, 2010 9:31 pm

by AndyB » Mon Oct 17, 2011 2:22 am

Thanks everybody guys...For your time..

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Oct 17, 2011 3:49 am

IMO: B, wish to get such questions in the real CAT

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