A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya

Question

Source: e-GMAT

A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 yards race by 100 yards, whereas C can beat D in a 600 yards race by 40 yards. Select the values of  'A beats C' , & ' B beats D'  by yards in a 200 yards race in the table that are consistent with the information provided. 
Make only two selections, one in each column.

-Shalabh

egmat · Accepted Answer

Hi punwish,

That's the correct answer. Yes, you are right this is a longer method to approach the question. I think the approach below is smarter one.

We can find out the continued ratios of all 4 players.

--A--:---B--:---C--:---D----
400 : 340
------:850 : 750
------:-----: 600 : 560 
------------------------------------
400 : 340 : 750/850*340 : --
400 : 340 : 300 : 560/600*300
 400 : 340 : 300 : 280

So. we can infer that A beats C by 100 yards in a 400 yard race, so it will beat C by 50 yards in a 200 yard race.

Similarly, we can infer that B beats D by 60 yards in 340 yard race, so it will beat D by (340-280)/340*200 = ~35 yards in a 200 yard race.

Meanwhile, don't forget to attend the SC session on Saturday. Please find the link below:

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-Shalabh

punwish · Answer

This is the longer version of solution , there is a quick way to do it also :

Lets say As is the speed of A , Bs is the speed of B and similarly Cs is for C & Ds is for D.

if A took T1 time to finish the 400 yards race , so in the same time B will cover 340 yards

Therefore, we can say that T1 = 400/As and T1 = 340/Bs (Speed = Distance/Time or Time = Distance/speed ).

T1 = 400/As = 340/Bs => As/Bs = 400/340 or As/Bs = 20/17

Similarly , we can get

Bs/Cs = 17/15 & Cs/Ds= 15/14

therefore we can say , As/Cs = 4/3 ( As = 20/17 * Bs = 20/17 * 17/15 * Cs = 20/15 Cs

Lets assume to complete a 200 yards race A took time T , then

As=200/T or T = 200/As , in the same time C will cover X distance , so X = Cs * T (Distance = Speed * time)

Therefore X = Cs * 200/As ( from above we knw that As/Cs = 4/3 )

X = 200 / (As/Cs) = 200 / (4/3) = 150.

Thereby we can say that A will beat C in a 200 yards race by 50 yards.

Similarly we can get that B will beat D in a 200 yards race by 35 yards.

crazypriya · Answer

50 and 35
just find out by how much each beats other in 200yards race...
easy one....

egmat · Answer

Thank you Shashank. By the way do not forget to attend following event this weekend to learn how to improve by up to 70 points in 25 days. Pl. click to know more.

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-Shalabh Jain

jabhatta2 · Answer

Hi - I really like this method but i have a question Given all the ratio's are equalized now (highlighted in purple font as continued ratio's) , i thought the green took place over the 400 yard race, not over a 340 yard race Why is the green taking over a 340 yard race and not over a 400 yard race All the ratio's are equlized and given we are starting from A to B which took place over a 400 yard race, i think B beat D over a 400 yard race and not over a 340 yard race Please let me know

;(

harishramesh · Answer

Hey everyone, I used a different approach which took around 2 mins for me with the calculator.

Step 1: A beats B by 60 yards in a 400-yard race

If A beats B by 60 yards in 400 yards, 
then in  half  that distance (200 yards), the margin would also be  halved :
60/ 2=30 yards
So  A beats B by 30 yards in a 200-yard race .

Step 2: B beats C by 100 yards in an 850-yard race

To scale this down to 200 yards, we find the common diviser:
850/200=4.25
So the margin B beats C by in 200 yards is:
1004.25≈23.53 yards

Step 3: A beats C

We already know:
 
 A beats B by  30 yards  
 B beats C by  ~23.53 yards   
So A beats C by:
30+23.53≈53.53

The closest option available:  50 yards for first column

Step 4: B beats D
Similarly:
 
 B beats C by  100 yards in 850  
 C beats D by  40 yards in 600   
Let’s scale both down to 200 yards.

First, B beats C:
 Already calculated →  23.53 yards  over 200
Then, C beats D by 40 yards in 600 yards
40/3=13.33 yards in 200 yards

Now, B beats D =
23.53 (B over C) + 13.33 (C over D) = 36.86 ~ 35 
So the  correct selection in the second column  is:  35

A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya

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GMAT Two-part Analysis (TPA) Questions

A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya

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