Andy is considering enlarging his existing garden, which is rectangula

Question

Andy is considering enlarging his existing garden, which is rectangular. He has two options. If he increases the length of the existing garden by 5 m and does not change the width, then the area of the enlarged rectangular garden will be twice the area of the existing garden. On the other hand, if he increases the width of the existing garden by 2 m and does not change the length, then the area of the enlarged rectangular garden will be 1.5 times the area of the existing garden.

From the Dimensions column in the following table, identify a length and a width, in meters, for Andy's existing garden that are consistent with Andy's two options. Make only two selections, one in for each column.

Sajjad1994 · Accepted Answer

Official Explanation

RO1

For any rectangle, the area is equal to the length (L) times the width (W). In Andy's garden, a length 5 m longer would yield an area twice as large. In other words, (L + 5)W = 2LW. Distributing the W gives LW + 5W = 2LW, and subtracting LW from both sides gives 5W = LW.

We are also told that a width 2 m longer would yield an area 1.5 times as large. In other words, L(W + 2) = 1.5LW. Distributing the L gives LW + 2L = 1.5LW, and subtracting 1.5LW from both sides gives 2L = 0.5LW. Multiplying both sides of the equation by 2 gives 4L = LW.

Thus, 5W = LW and 4L = LW, so 5W = 4L. Dividing both sides of the equation by 5 gives \(W=\frac{4}{5}L.\) The following table shows what the width of Andy’s garden would be for each of several possible lengths:

The only value for the width that is one of the possible options is 4. The corresponding length is 5.

The correct answer is 5.

RO2

The table provided in the analysis of RO1 shows that if the length is 5, the corresponding width is 4.

The correct answer is 4

Show Spoiler

Attachment:

2.jpg [ 11.45 KiB | Viewed 14018 times ]

Sumi1010 · Answer

Let's consider that length of the garden be L meters and width be W meters.

From the given information :

Increase the length by 5 meter and keep width unchanged . 
Area : (L+5)(W) = 2 x (L)(W) --- 1

Increase the width by 2 meter and keep length unchanged . 
Area : (L)(W+2) = 1.5 x (L)(W). --- 2

From 1 and 2 together (putting 2 into 1)
3x(L+5)(W) = 4x (L)(W+2)
3LW + 15W = 4LW + 8L
L(W+8) = 15W 
 L = 15W/(W+8)

Let W= 3, L will be 45/11
 W=4, L will be 60/12 = 5 
W=5, L will be 75/13
W= 6, L will be 90/14
W= 7, L will be 105/15 = 7 (For two selections,one in for each column L and W can't be same)
 W=8 L will be 120/16= 7.5  (width can't be greater than Length)

Hence, 
 Length = 5
Width = 4

TarunKumar1234 · Answer

Let's say length= l and width=w, Area= l*w

Equation1: (l+5)*w=2*lw so, l=5= Length
Equation2: l*(w+2) =1.5*lw, so, w=4= Width

jhavyom · Answer

Andy is considering enlarging his existing garden, which is rectangular. He has two options. If he increases the length of the existing garden by 5 m and does not change the width, then the area of the enlarged rectangular garden will be twice the area of the existing garden. On the other hand, if he increases the width of the existing garden by 2 m and does not change the length, then the area of the enlarged rectangular garden will be 1.5 times the area of the existing garden.

Let the existing length and width be x and y respectively.

If he increases the length of the existing garden by 5 m and does not change the width, then the area of the enlarged rectangular garden will be twice the area of the existing garden

(x+5)y = 2xy
or, x = 5 m

if he increases the width of the existing garden by 2 m and does not change the length, then the area of the enlarged rectangular garden will be 1.5 times the area of the existing garden

x(y+2) = 1.5(xy)
or, y = 4 m

Therefore, existing garden's dimensions are:
Length (x) = 5 m
Width (y) = 4 m

Deepakjhamb · Answer

answer 1 :

(l+5)*w = 2lw - eq 1

l* (w+2) = 3/2lw -eq 2

from eq 1 l = 5 and from eq2 w= 4

rocky620 · Answer

Let the original Length = " l ", Breadth = " b "
Original ares = l*b

Case-1

Increasing the length by 5, keeping the breadth same the area will be double the original

(l+5)*b = 2l*b
lb + 5b = 2lb
5b = lb
  l=5

Case-2

Increasing the breadth by 2, keeping the length same the area will be 1.5 times the original

l*(b+2) = 1.5*l*b
lb + 2l = 1.5lb
Replacing l with 5 (from case-1)
5b+10 = 7.5b
10=2.5b
  b=4

l=5, b=4

Sajjad1994 · Answer

This is an easy question just checking the test taker’s basic math knowledge, OA is updated that is (Length (m): 5 Width (m): 4

Good reasoning by  Sumi1010  and  jhavyom

Deepakjhamb  Not explained well subjectively but yes the answer is correct. We can solve this question without any math involved but the math route is faster.

Good Luck

RahulJain293 · Answer

I tried as below ..

We know  L*B = A ----- eq 1

Question says,
(L+5)*B = 2A 
LB + 5B = 2A

(Sub eq 1 above)
A + 5B = 2A
 A = 5B   --- eq 2

Also, L(B+2) = 1.5A
solving we get  A = 4L  --- eq3

Equating 2 & 3, we get

4L = 5B
Hence, L/B = 5/4

Therefore, Length = 5 and Breadth = 4

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Andy is considering enlarging his existing garden, which is rectangula

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 Two-part Analysis (TPA) Questions

Andy is considering enlarging his existing garden, which is rectangula

Prep Toolkit

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