Quantum - Word Problems

Question 1

Basic distance relationship?

Answer 1

Distance = Rate × Time (d = rt). If two variables are known, solve for the third. Always isolate the unknown before plugging numbers.

Question 2

If two objects travel toward each other, how do you combine rates?

Answer 2

Add their speeds because the gap closes from both sides. Example: 40 mph + 60 mph = 100 mph closing rate.

Question 3

If two objects travel in the same direction, how combine rates?

Answer 3

Subtract the slower from the faster. This gives the relative speed (how fast one catches the other).

Question 4

How do you calculate average speed over a round trip?

Answer 4

Use total distance ÷ total time. Do NOT average the two speeds unless distances are identical — and even then, use harmonic mean logic.

Question 5

If speed increases while distance fixed, what happens to time?

Answer 5

Time decreases proportionally because t = d/r. Double rate → half the time.

Question 6

Core work formula?

Answer 6

Work = Rate × Time. Rate is usually “fraction of job per hour.”

Question 7

If A completes a job in 4 hours, what is A’s hourly rate?

Answer 7

1/4 of the job per hour. Always convert time-to-complete into rate first.

Question 8

If A and B work together, how combine their efforts?

Answer 8

Add their rates, not their times. Combined rate = 1/A time + 1/B time.

Question 9

What is the biggest work problem trap?

Answer 9

Adding completion times instead of adding rates. Work problems are always rate-based.

Question 10

Percent increase formula?

Answer 10

(New − Old) ÷ Old. The denominator is always the original value.

Question 11

If price increases 20% then decreases 20%, is it back to original?

Answer 11

No. The second percent applies to a different base number, so net result is lower.

Question 12

How do you calculate 18% of 250 quickly?

Answer 12

10% = 25 5% = 12.5 3% = 7.5 Add strategically instead of multiplying directly.

Question 13

What is a percent-of-percent trap?

Answer 13

Always clarify: percent of what base? Percent change problems frequently shift bases.

Question 14

How do you set up mixture problems?

Answer 14

Amount × Concentration = Pure substance. Add pure parts together before solving.

Question 15

Why must percent be converted to decimal?

Answer 15

Because equations require multiplication form (e.g., 30% → 0.30).

Question 16

What does the final mixture equation represent?

Answer 16

Total pure substance before mixing = total pure substance after mixing.

Question 17

If ratio is 4:5 and total is 45, how solve?

Answer 17

Add parts (9 total). Divide total by 9 to find unit value. Multiply back to get each component.

Question 18

If both parts of ratio double, does ratio change?

Answer 18

No. Ratio reflects relationship, not absolute size.

Question 19

Common ratio trap?

Answer 19

Confusing part-to-part with part-to-whole.

Question 20

How represent three consecutive integers?

Answer 20

n, n+1, n+2. Always define smallest as n.

Question 21

How represent even integers?

Answer 21

2n. This ensures automatic even structure.

Question 22

How represent odd integers?

Answer 22

2n + 1.

Question 23

Probability formula?

Answer 23

Favorable outcomes ÷ total outcomes. Ensure events are equally likely.

Question 24

How combine independent probabilities?

Answer 24

Multiply them because both events must occur.

Question 25

What is complement rule?

Answer 25

1 − P(event). Often easier to calculate “not happening.”

Question 26

Mean formula?

Answer 26

Sum ÷ number of values. Outliers strongly affect it.

Question 27

Median strategy when even number of terms?

Answer 27

Average the two middle numbers.

Question 28

What happens to mean if one value increases?

Answer 28

Mean increases proportionally.

Question 29

When use permutation formula?

Answer 29

When order matters.

Question 30

When use combination formula?

Answer 30

When order does not matter.

Question 31

“Of” translates to?

Answer 31

Multiply. Example: 30% of x → 0.30x

Question 32

“More than” translates to?

Answer 32

Add after. Example: 5 more than x → x + 5

Question 33

“Less than” translates to?

Answer 33

Subtract from. Example: 5 less than x → x − 5

Question 34

If question feels messy, what first?

Answer 34

Define variables clearly before solving.

Question 35

When should you plug in numbers?

Answer 35

When answer choices are numeric and algebra is messy.

Question 36

When should you back-solve from answers?

Answer 36

When answer choices are simple numbers and equation complex.

Question 37

What’s the elite word-problem approach?

Answer 37

Translate → Write equation → Pause → Then solve.

Question 38

What signals overcomplication?

Answer 38

You are calculating multiple layers without a clear equation.

Question 39

If answer choices are far apart, what do you do?

Answer 39

Estimate first to eliminate.

Question 40

If two answers close, what do you do?

Answer 40

Calculate precisely.