If x is a number satisfying 2

Question

If x is a number satisfying 2 < x < 3 and y is a number satisfying 7 < y < 8, which of the following expressions will have the largest value?

A.  x^2y

B.  xy^2

C. 5xy

D.  \frac{4x^2y}{3}

E.  \frac{x^2}{y}

chetan2u · Answer

since we have to find the largest of given expression we will have to TEST all of the choices..

A.  x^2y .........lets see the next

B.  xy^2 ........y>x so  xy^2>x^2y ... so B till now

C. 5xy.......... in B xy is bein multiplied by something between 7 and 8 but in C it is being multiplied by 5, SO B is bigger

D.  \frac{4x^2y}{3} ...... y>2x so x^2y multiplied by 4/3 will still not make it bigger than xy^2

E.  \frac{x^2}{y} .... division is involved, so surely is the lowest

B is the winner

SECOND way
since all choices are containing x and y, it will suffice here to take LARGEST value of x and SMALLEST value of y
so x=3 and y=7..
substitue and you will get B as the answer

septwibowo · Answer

I answer B.

Arrived B with plugging x=3 and y=8.

KarishmaB · Answer

To get the largest product, each variable that is multiplied should be largest and the one that divides should be smallest. The largest value x can take is slightly less than 3 and the largest value that y can take is slightly less than 8

A.  x^2y

The largest value of this is about 3*3*8

B.  xy^2

The largest value of this is about 3*8*8

C. 5xy

The largest value of this is about 5*3*8

D.  \frac{4x^2y}{3}

The largest value of this is about 4*3*3*8/3 = 4*3*8

E.  \frac{x^2}{y}

The largest value of this is about 3*3/7

A simple comparison shows that (B) is the greatest.

generis · Answer

You can plug in values. There are three choices:

1) mixed (improper) fractions, e.g. for x,  \frac{5}{2} ;

2) decimals, e.g. for x, 2.5 (IMO easier than fractions); or

3) whole numbers, by far the easiest choice. This choice violates the stated conditions.

But all the operations in the answer choices involve multiplication and/or division.

In such cases, whole numbers and improper fractions greater than one all behave the same way (e.g., when squared, their value is greater).

Pick x and y values both on the high end or low end. (It might not matter, but it's safer.)

Let x = 2
Let y = 7

A.  x^2y = (4 * 7) = 28

B.  xy^2 = (2 * 49) = 98

C.  5xy = (5)(14) = 70

D.  \frac{4x^2y}{3} =
\frac{(4)(4)(7)}{3}  = 37 + a little

E.  \frac{x^2}{y} =
\frac{4}{7}

These answers are not close. The greatest value is

Answer B

II. Decimal values  - in case there's doubt: answers for x = 2.1, y = 7.1

A.  x^2y  = 28 + a little

B.  xy^2  = 100 + a little

C. 5xy = about 75

D.  \frac{4x^2y}{3}  = = a little less than 40

E.  \frac{x^2}{y} = about  \frac{4}{7}

The whole numbers and the decimals behaved exactly the same way. These numbers are not close either.

Answer B

ScottTargetTestPrep · Answer

First, notice that y is greater than x, and y^2 is significantly greater than x^2. This observation allows us to immediately suspect that B is the correct answer because it is the only choice that contains y^2. We can immediately rule out choices A, C, and E without doing any calculations because each of them contains the relatively small value of x^2, and none of them contain the large value y^2.

Let’s consider choice D, which multiplies the relatively small value of (x^2)(y) by 4/3, which makes it larger. But multiplication by 4/3 is not enough to make (x^2)(y)(4/3) greater than choice B.

Answer: B

Plunkster82 · Answer

I got B, but perhaps I was totally inefficient which might be a cause for my propensity to make lots of stupid mistakes. 
-Even though x cannot equal 3 and y cannot equal 8, they can be infinitely close to each number. So I used the outer bounds of each range and plugged them into each number. B produced the largest result. 
-For A, I got 72.
-For B, I got 192.
-For C, I got 120
-For D, I got 96,
-E, I didn't calculate because it's some small fraction.

-This problem could have been made a lot harder with the inclusion of negatives as we would have to determine whether certain exponents produce a negative or positive.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x is a number satisfying 2 < x < 3 and y is a number satisfying 7 <

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions