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Scoring 715 on the GMAT Focus Edition requires more than just learning formulas, memorizing concepts, or solving hundreds of questions. In this episode, Nishant shares how he improved his GMAT preparation by focusing on application of concepts, and more. 
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Races – Complete GMAT Guide
Race questions are simply Distance = Speed × Time questions in disguise.
Most race questions become easy if you understand:
• Head starts
• Dead heats
• Beating by distance
• Beating by time
• Speed ratios
Example:
Start -------------------------------- Finish
Whenever a head start is given, place racers accordingly.
Why?
Race questions are easier when you think in terms of positions rather than equations.
A gives B a 10 m head start in a 100 m race.
Initial positions:
Start A----B---------------------------Finish
A runs 100 m.
B runs only 90 m because B starts 10 m ahead.
Key idea:
Both start at the same time.
They do not start from the same position.
Type 2: Time Head Start
A gives B a 1 minute head start.
Timeline:
12:00 B starts
12:01 A starts
Both start from the same position.
Key idea:
They start at different times.
They do not start from different positions.
Quick distinction:
Distance head start:
• Same time
• Different positions
Time head start:
• Different times
• Same position
Finish
A |
B |
Key translation:
Time of A = Time of B
Most race questions eventually create a dead heat condition.
Whenever you see:
"finish together"
"tie"
"dead heat"
Immediately think:
Time of A = Time of B
Suppose race length = 1000 m.
A beats B by 20 m.
When A reaches the finish line:
Finish
A |
B is still 20 m away from the finish line.
Meaning:
When A has run 1000 m,
B has run only 980 m.
Important:
Always freeze the race when the winner finishes.
Do not think about when B eventually finishes.
A Beats B By Time
Suppose A beats B by 2 minutes.
If A finishes at 12:10,
B finishes at 12:12.
Meaning:
At 12:10, B still requires 2 more minutes at B's own speed to finish.
Key difference:
Beats by distance → compare positions.
Beats by time → compare finishing times.
If:
A:B = 20:17
then in the same amount of time:
A covers 20 units.
B covers 17 units.
Examples:
A = 20, B = 17
A = 40, B = 34
A = 200, B = 170
This single idea solves most race questions.
Important:
Speed ratio gives distance ratio only when time is equal.
Do not treat it as a time ratio.
A's speed is 20/17 times B's speed.
Therefore:
A:B = 20:17
Interpretation:
In equal time:
A covers 20 units.
B covers 17 units.
Suppose race length is 20 units.
When A reaches the finish line:
A = 20
B = 17
B is behind by:
20 − 17 = 3 units
To make them finish together, B should start 3 units ahead.
Start
A---B-----------------
Then:
A still runs 20 units.
B runs only 17 units.
Since 20 and 17 take the same time at speeds 20:17, they finish together.
Therefore head start:
3/20 of race length
Shortcut:
If speed ratio:
A:B = a:b
and race ends in a dead heat,
Head Start = (a − b)/a
Example:
A:B = 20:17
Head Start = (20 − 17)/20 = 3/20
Example:
A:B = 20:17
B must beat A by 20% of the race length.
Step 1
Choose race length = 25.
Why?
20% of 25 = 5
Easy calculations.
Step 2
If B beats A by 20%,
then when B finishes,
A is still 5 units away from the finish line.
Therefore A has covered:
25 − 5 = 20
units.
Step 3
Speed ratio is 20:17.
So whenever A covers 20 units,
B covers 17 units.
Step 4
But B must actually be at the finish line, i.e. at 25 units.
Therefore B needs an extra:
25 − 17 = 8
units.
That extra distance must come from a head start.
Head Start = 8/25
Head Start Percentage = 32%
Answer = 32%
Important Visualization
Whenever a runner beats another by x meters:
Freeze the race at the exact moment the winner finishes.
Then ask:
Where is the loser?
This visualization prevents most mistakes.
Convert speeds into a ratio.
Example:
20/17 becomes 20:17
Step 2
Imagine equal time.
Ask:
How much distance does each cover in the same time?
Step 3
Use a convenient race length.
Often use:
20
25
100
L
Step 4
Draw starting positions.
Examples:
Start A---B---------
or
Start A,B-----------
Step 5
Draw ending positions.
Example:
A finished
B 3 m behind
or
B finished
A 20% behind
Step 6
Translate the picture into an equation.
Most race questions become straightforward after the picture is clear.
Common GMAT Traps
Trap 1: Confusing Time Head Start and Distance Head Start
Always ask:
Did B start earlier?
or
Did B start ahead?
Trap 2: Using Speed Ratio as Time Ratio
Wrong.
Speed ratio gives distance ratio only when time is equal.
Trap 3: Not Freezing the Race
For:
"A beats B by 20 m"
Freeze the race when A finishes.
Do not think about what happens afterward.
Trap 4: Using Actual Race Length Immediately
Often easier to choose:
20
25
100
instead of using the real length.
Most Important Formulas
Dead Heat
If:
A:B = a:b
Head Start = (a − b)/a
A Beats B By Distance
If:
A:B = a:b
then when A finishes,
B has completed:
b/a
of the race.
Distance by which A beats B:
1 − b/a
= (a − b)/a
of the race.
Quick Memory
If:
A:B = 20:17
then whenever A finishes,
B is short by:
20 − 17 = 3 parts.
This is the single most useful race observation for GMAT questions because many race problems reduce to finding those "missing parts."
Race questions are simply Distance = Speed × Time questions in disguise.
Most race questions become easy if you understand:
• Head starts
• Dead heats
• Beating by distance
• Beating by time
• Speed ratios
- Always Draw a Track
Example:
Start -------------------------------- Finish
Whenever a head start is given, place racers accordingly.
Why?
Race questions are easier when you think in terms of positions rather than equations.
- Two Types of Head Start
A gives B a 10 m head start in a 100 m race.
Initial positions:
Start A----B---------------------------Finish
A runs 100 m.
B runs only 90 m because B starts 10 m ahead.
Key idea:
Both start at the same time.
They do not start from the same position.
Type 2: Time Head Start
A gives B a 1 minute head start.
Timeline:
12:00 B starts
12:01 A starts
Both start from the same position.
Key idea:
They start at different times.
They do not start from different positions.
Quick distinction:
Distance head start:
• Same time
• Different positions
Time head start:
• Different times
• Same position
- Dead Heat
Finish
A |
B |
Key translation:
Time of A = Time of B
Most race questions eventually create a dead heat condition.
Whenever you see:
"finish together"
"tie"
"dead heat"
Immediately think:
Time of A = Time of B
- Two Ways to Beat Someone
Suppose race length = 1000 m.
A beats B by 20 m.
When A reaches the finish line:
Finish
A |
B is still 20 m away from the finish line.
Meaning:
When A has run 1000 m,
B has run only 980 m.
Important:
Always freeze the race when the winner finishes.
Do not think about when B eventually finishes.
A Beats B By Time
Suppose A beats B by 2 minutes.
If A finishes at 12:10,
B finishes at 12:12.
Meaning:
At 12:10, B still requires 2 more minutes at B's own speed to finish.
Key difference:
Beats by distance → compare positions.
Beats by time → compare finishing times.
- Golden Rule of Race Questions
If:
A:B = 20:17
then in the same amount of time:
A covers 20 units.
B covers 17 units.
Examples:
A = 20, B = 17
A = 40, B = 34
A = 200, B = 170
This single idea solves most race questions.
Important:
Speed ratio gives distance ratio only when time is equal.
Do not treat it as a time ratio.
- Dead Heat Using Speed Ratios
A's speed is 20/17 times B's speed.
Therefore:
A:B = 20:17
Interpretation:
In equal time:
A covers 20 units.
B covers 17 units.
Suppose race length is 20 units.
When A reaches the finish line:
A = 20
B = 17
B is behind by:
20 − 17 = 3 units
To make them finish together, B should start 3 units ahead.
Start
A---B-----------------
Then:
A still runs 20 units.
B runs only 17 units.
Since 20 and 17 take the same time at speeds 20:17, they finish together.
Therefore head start:
3/20 of race length
Shortcut:
If speed ratio:
A:B = a:b
and race ends in a dead heat,
Head Start = (a − b)/a
Example:
A:B = 20:17
Head Start = (20 − 17)/20 = 3/20
- Beating By Distance
Example:
A:B = 20:17
B must beat A by 20% of the race length.
Step 1
Choose race length = 25.
Why?
20% of 25 = 5
Easy calculations.
Step 2
If B beats A by 20%,
then when B finishes,
A is still 5 units away from the finish line.
Therefore A has covered:
25 − 5 = 20
units.
Step 3
Speed ratio is 20:17.
So whenever A covers 20 units,
B covers 17 units.
Step 4
But B must actually be at the finish line, i.e. at 25 units.
Therefore B needs an extra:
25 − 17 = 8
units.
That extra distance must come from a head start.
Head Start = 8/25
Head Start Percentage = 32%
Answer = 32%
Important Visualization
Whenever a runner beats another by x meters:
Freeze the race at the exact moment the winner finishes.
Then ask:
Where is the loser?
This visualization prevents most mistakes.
- Standard GMAT Race Framework
Convert speeds into a ratio.
Example:
20/17 becomes 20:17
Step 2
Imagine equal time.
Ask:
How much distance does each cover in the same time?
Step 3
Use a convenient race length.
Often use:
20
25
100
L
Step 4
Draw starting positions.
Examples:
Start A---B---------
or
Start A,B-----------
Step 5
Draw ending positions.
Example:
A finished
B 3 m behind
or
B finished
A 20% behind
Step 6
Translate the picture into an equation.
Most race questions become straightforward after the picture is clear.
Common GMAT Traps
Trap 1: Confusing Time Head Start and Distance Head Start
Always ask:
Did B start earlier?
or
Did B start ahead?
Trap 2: Using Speed Ratio as Time Ratio
Wrong.
Speed ratio gives distance ratio only when time is equal.
Trap 3: Not Freezing the Race
For:
"A beats B by 20 m"
Freeze the race when A finishes.
Do not think about what happens afterward.
Trap 4: Using Actual Race Length Immediately
Often easier to choose:
20
25
100
instead of using the real length.
Most Important Formulas
Dead Heat
If:
A:B = a:b
Head Start = (a − b)/a
A Beats B By Distance
If:
A:B = a:b
then when A finishes,
B has completed:
b/a
of the race.
Distance by which A beats B:
1 − b/a
= (a − b)/a
of the race.
Quick Memory
If:
A:B = 20:17
then whenever A finishes,
B is short by:
20 − 17 = 3 parts.
This is the single most useful race observation for GMAT questions because many race problems reduce to finding those "missing parts."
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