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805+ (Hard)|   Math Related|      
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egmat
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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya Updated on: 02 Oct 2023, 23:10
Originally posted by egmat on 01 Jan 2013, 22:48.
Last edited by BottomJee on 02 Oct 2023, 23:10, edited 6 times in total.
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A beats
C: 50 B beats
D: 35
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

54% (03:26) correct 46% (03:29) wrong based on 340 sessions

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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
A beats
C 		B beats
D 		-------
15
25
35
45
50
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A beats
C: 50 B beats
D: 35
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egmat
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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya 04 Jan 2013, 01:19
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punwish
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.
Show more

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:




-Shalabh
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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya 03 Jan 2013, 18:50
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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.
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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya 08 Jan 2013, 22:26
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50 and 35
just find out by how much each beats other in 200yards race...
easy one....
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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya 08 Jan 2013, 23:21
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Shashank3016
egmat

--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

That was a very quick method Shalabh. Thanks!
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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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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya 14 Nov 2017, 18:19
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egmat
punwish
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.

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:




-Shalabh
Show more

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 :( ;(
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A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 ya 18 Jun 2025, 03:27
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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

egmat
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
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