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GMAT Club World Cup 2026 (Day 1): Along a straight coastal road, four

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RDM42

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06 Jul 2026, 21:18

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H<M<R<S

Ridge is 3 times as far from Harbor as it is from Summit
HR=3RS
Let, RS=a
HR=3a _____(1)
HS=HR+RS= 3a+a=4a

Maple is 4 times as far from Ridge as it is from Harbor
MR=4HM
Let, MH=b
MR=4b
HR=HM+MR=b+4b=5b ____(2)

From 1&2
3a=5b

HS=4b
MS=HS-HM= 4a-3a/5=17a/5

MS/HS= (17a/5)/(4a) =17/20

D

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Let the stops be H, M, R, S.

Condition 1: R is 3 times as far from H as it is from S - so if distance between R and S is x then distance between R and H is 3x and total distance between H and S comes to be 4x.

Condition 2: M is 4 times as far from R as it is from H - so if the distance between M and H is y then distance between M and R is 4y and total distance between H and R is 5y.

we need to find ratio of distance of M-S to H-S
distance between M-S: M-R (4y) + R-S (x)
distance between H-S: 4x
so ratio becomes (4y+x)/(4x) ....... (1)

from above conditions, distance H-R equals to both 3x and 5y(highlighted) so this gives y=(3/5)x, put this value in (1) and we get ratio as 17/20.

Bunuel

Along a straight coastal road, four stops, Harbor, Maple, Ridge, and Summit, appear in that order. Ridge is 3 times as far from Harbor as it is from Summit. Maple is 4 times as far from Ridge as it is from Harbor. What fraction of the distance from Harbor to Summit is the distance from Maple to Summit?

A. 3/20
B. 1/4
C. 2/5
D. 17/20
E. 20/17

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06 Jul 2026, 22:19

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HMRS
RS = x
HR = 3x
=> HS = 4x
MR = 4y
HM = y
=> HR = 5y

=> 3x = 5y

MS/HS = 1- HM/HS
= 1 - y/4x
= 1 - 3x/20x
= 17/20

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First we visualize a line segment with four points on it - H,M,R and S. Now HM = y and MR = 4y, so HM:MR = 1:4. Similarly, HR = 3x and RS = x, so HR:RS satisfies 3:1. We want MS:HS. This can be expressed as equation 1: (4y+x)/4x. But, MS is also equal to 4x-y. Putting 4y+x=4x-y, we get y=3x/5. Substituting that in equation 1, we get rid of x, and get 17:20.

Bunuel

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H M R S. Denoting each destination by one letter. The distance from H to R is three times as much as the distance from R to S. Define the distance from R to S as X, so the distance from H to R is 3X.

The distance from M to R is four times greater than the distance from H to M. Define the distance from H to M as Y, so the distance from M to R is 4Y.

The distance from H to S is 3X + X = 4X. the distance from M to S is 4Y + X.
Their ratio is (4Y + X) / 4X-> 4Y/4X + X/4X = Y/X + 1/4 =
Now, 4Y + Y = 3X->5Y=3X-> Y/X = 3/5
So, 3/5 + 1/4 = 12/20 + 5/20 = 17/20-> Option D)

Bunuel

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Ans D
Solution in picture attached.

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Let Harbor be H , Maple be M, Ridge be R, Summit be S

Let RS=x, HR=3x ,HM=3y and MR=4y

Total distance = x+3x=4x

MS=HS-HM

=17x/5

Required fraction = (17x/5)/4x ==> 17/20

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Ridge to Summit = X
Harbor to Ridge = 3*X
Harbor to Maple = Y
Maple to Ridge = 4*Y

We also know that:
Harbor to Ridge = 3*X = 4*Y+Y = 5Y -> Y = 3*X/5

Maple to Summit = 4*Y+X = 4*3*X/5 + X = 17*X/5
Harbor to Summit = 3*X+X = 4*X

(Maple to Summit)/(Harbor to Summit) = (17*X/5) / 4*X = 17/20

The answer is D

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H, M, R, S

R-S = m -> H-R = 3m
H-M = n -> M-R = 4n

H-R = 3m = 5n -> n = 3m/5

(M-S)/(H-S) = (4n+m)/4m = (12m/5 + m)/4m = (17/5)/4 = 17/20

The correct answer is D

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Bunuel

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imagine the distance from Harbor to Ridge is split into 5 equal parts.

Because Maple is 4 times as far from Ridge as it is from Harbor, the distance from Harbor to Maple is 1 part and Maple to Ridge is 4 parts.

Now, Ridge is 3 times as far from Harbor as it is from Summit. So if Harbor to Ridge is 5 parts, then Ridge to Summit is 5 ÷ 3 parts. The whole distance from Harbor to Summit is:

*Harbor to Ridge: 5 parts
*Ridge to Summit: 5/3 parts

Together, that is 20/3 parts.

The distance from Maple to Summit is:

*Maple to Ridge: 4 parts
*Ridge to Summit: 5/3 parts

Together, that is 17/3 parts.

So Maple to Summit compared to Harbor to Summit is: 17/3 divided by 20/3 = 17/20

Answer is D. 17/20.

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According to the question, Harbor, Maple, Ridge and Summit appear in order. For simplicity we can plot a line with 4 points and take the distances between 2 points as their initials, for example - HM for Harbor-Maple, MR for Maple-Ridge and so on.

Given data, Ridge is 3 times as far from Harbor as it is from Summit. Thus, we can say $HR = 3RS$ - equation 1
Similarly, Maple is 4 times as far from Ridge as it is from Harbor - $MR = 4HM$ - equation 2

Now, in our line diagram we can see that $HR = HM + MR$
from equation 1 - $RS = \frac{1}{3}(HM + MR)$ - equation 3

Let us now check for HS and MS -

$HS = HM + MR + RS$
$HS = HM + MR + \frac{1}{3}(HM + MR)$ from equation 3
$HS = \frac{4}{3}(HM + MR)$
$HS = \frac{4}{3}(HM + 4HM)$ from equation 2
$HS = \frac{20}{3}HM$

$MS = MR + RS$
$MS = MR + \frac{1}{3}(HM + MR)$ from equation 3
$MS = 4HM + \frac{5}{3}HM$ from equation 2
$MS = \frac{17}{3}HM$

We need to find (k) in $k(HS) = MS$ ie, the fraction of the distance from Harbor to Summit equal to distance from Maple to Summit.
dividing HS with MS - $\frac{HS}{MS} = \frac{20}{17}$ therefore, $\frac{17}{20}HS = MS $

answer is $\frac{17}{20}$

Bunuel

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07 Jul 2026, 00:23

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let assume,
H........y.......M........4y........R................S
H..................3x................ R......x.......S

to find: MS/ HS=?
from what assumed, 3x=5y or y=3x/5
MS= 4y+x = 4*3x/5 +x = 12x/5 +x =17x/5
HS= 4x

So, MS/HS= (17x/5)/ 4x = 17/20

Bunuel

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07 Jul 2026, 00:23

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Ridge divides HS into 4 parts 3:1
Maple divides HR into 5 parts 4:1

lets assume the total distance to be 4*5 = 20
HR is 3 times to H So R = 3/4 * 20 ie 15 miles

RS= 5 Miles

Maple is 4 times from R So..
MR = 4/5*15 = 12
HM = HR - MR = 15 - 12 = 3

MS = HS - HM = 20 - 3= 17

Final answer: MS/HS = 17/20

Bunuel

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ans: d

H M R S

MS/HS =?

RH = 3 RS
MR = 4MH

so based on this distance b/w:
R to S = a
H to R = 3a
H to M = y
M to R = 4y

so 3a = 5y
y = 3a/5

MS = 4y + a
HS = 4a

so solving all that we get 17/20.

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07 Jul 2026, 00:50

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Let Ridge to Summit =1 unit

Then Harbor to Ridge = 3 units, so Harbor to Summit = 4 units

Now let Harbor to Maple = x. Since Maple to Ridge is 4 times Harbor to Maple, Maple to Ridge = 4x

So, x + 4x = 5x
-> 5x= 3
-> x = 3/5

Therefore, Maple to Summit = 4x + 1 => 12/5 +1 = 17/5

Required fraction = (17/5) / 4 = 17/20

Ans : D

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07 Jul 2026, 01:13

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Let RS=x
Then HR=3x

Let HM=Y
MR=4Y

Now HR=HM+MR
On solving we get y=3x/5

we have to find -> (4y+x)/(4x)
On solving we get 17/20

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Here's how I did it-

Distance between H and R: R and S = 3:1
Distance between H and M: M and R = 1:4

Since we are given ratios, we assume some simple numbers- Distance between R and S = 10 km
So, distance between H and R is 30 km

Now, since M comes in between H and R and we are given the split between H and M and M and R- we can divide the 30 km into 1:4 = 6:24

So the fraction = Distance between M and S/ Distance between H and S

Distance between M and S = Distance from M to R and R to S = 24 + 10 = 34
Distance b/w H and S= 40 (H and R + R and S)

Fraction = 34/40= 17/20

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07 Jul 2026, 01:53

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1. Find the RS fraction
"Ridge is 3 times as far from Harbor as it is from Summit."

This means the H-to-R stretch is 3 parts, and the R-to-S stretch is 1 part.

The whole trip is 4 parts.

Therefore, RS = 1/4 of the total trip. (And HR = 3/4 of the total trip).

2. Find the MR fraction
"Maple is 4 times as far from Ridge as it is from Harbor."

This means Maple splits the HR stretch into 5 parts (1 part HM, 4 parts MR).

So, MR is 4/5 of the HR stretch.

To find what MR is compared to the whole trip, just multiply: 4/5 * 3/4 = 3/5 of the total trip.

3. Add them together
You need the distance from Maple to Summit (MS). Just add the two fractions together:

MS = MR + RS

MS = 3/5 + 1/4

Get a common denominator (20): 12/20 + 5/20 = 17/20

Once you get used to reading the ratios as fractions, you can do this entire calculation in your head in under 30 seconds.

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Here is my solution. I think the easiest. to solve this question is with a diagram.

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07 Jul 2026, 03:10

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Let distance between R and S is x and the distance between M and H is y.
22394.jpg
3x = y+4y = 5y
y = 3x/5

Let the fraction be f.
f = (Distance between M and S) / (Distance between H and S)
f = (4y + x)/(4x)
f = (4*3x/5 +x)/(4x)
f = 17/20

Hence, the answer is 17/20

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