Five students — Aditi, Bharat, Charu, Dev and Esha — took four tests (T1 to T4), each marked out of 50. All scores are whole numbers. The table shows some of the scores; a '?' marks a score that has been smudged out.
| Student | T1 | T2 | T3 | T4 | Average (4 tests) |
|---|---|---|---|---|---|
| Aditi | ? | 38 | ? | 35 | 40 |
| Bharat | 30 | ? | ? | 42 | 38 |
| Charu | 48 | ? | 32 | ? | 39 |
| Dev | 25 | 35 | 40 | ? | 36 |
| Esha | ? | 33 | 47 | 28 | ? |
| Class average | 37 | 38 | 40 | 37 | |
The class average for a test is the average of the five students' scores in that test.
| Student | T1 | T2 | T3 | T4 | Average (4 tests) |
|---|---|---|---|---|---|
| Aditi | ? | 38 | ? | 35 | 40 |
| Bharat | 30 | ? | ? | 42 | 38 |
| Charu | 48 | ? | 32 | ? | 39 |
| Dev | 25 | 35 | 40 | ? | 36 |
| Esha | ? | 33 | 47 | 28 | ? |
| Class average | 37 | 38 | 40 | 37 | |
The class average for a test is the average of the five students' scores in that test.
Question 1
Numerical answer
What was Aditi's score in T1?
Show answer and solution
Answer: 42
Totals: row totals = 4 × average (Aditi 160, Bharat 152, Charu 156, Dev 144); column totals = 5 × class average (T1 185, T2 190, T3 200, T4 185).
Peel off one unknown at a time:
1. Dev T4 = 144 − 100 = 44
2. Charu T4 = 185 − (35 + 42 + 44 + 28) = 36
3. Charu T2 = 156 − (48 + 32 + 36) = 40
4. Bharat T2 = 190 − (38 + 40 + 35 + 33) = 44
5. Bharat T3 = 152 − (30 + 44 + 42) = 36
6. Aditi T3 = 200 − (36 + 32 + 40 + 47) = 45
7. Aditi T1 = 160 − (38 + 45 + 35) = 42
8. Esha T1 = 185 − (42 + 30 + 48 + 25) = 40
| Student | T1 | T2 | T3 | T4 | Total |
|---|---|---|---|---|---|
| Aditi | 42 | 38 | 45 | 35 | 160 |
| Bharat | 30 | 44 | 36 | 42 | 152 |
| Charu | 48 | 40 | 32 | 36 | 156 |
| Dev | 25 | 35 | 40 | 44 | 144 |
| Esha | 40 | 33 | 47 | 28 | 148 |
Aditi's T1 score = 42.
Tip: start from a row or column that has only one '?' (Dev's row), then keep going through rows and columns in turn.
Peel off one unknown at a time:
1. Dev T4 = 144 − 100 = 44
2. Charu T4 = 185 − (35 + 42 + 44 + 28) = 36
3. Charu T2 = 156 − (48 + 32 + 36) = 40
4. Bharat T2 = 190 − (38 + 40 + 35 + 33) = 44
5. Bharat T3 = 152 − (30 + 44 + 42) = 36
6. Aditi T3 = 200 − (36 + 32 + 40 + 47) = 45
7. Aditi T1 = 160 − (38 + 45 + 35) = 42
8. Esha T1 = 185 − (42 + 30 + 48 + 25) = 40
| Student | T1 | T2 | T3 | T4 | Total |
|---|---|---|---|---|---|
| Aditi | 42 | 38 | 45 | 35 | 160 |
| Bharat | 30 | 44 | 36 | 42 | 152 |
| Charu | 48 | 40 | 32 | 36 | 156 |
| Dev | 25 | 35 | 40 | 44 | 144 |
| Esha | 40 | 33 | 47 | 28 | 148 |
Aditi's T1 score = 42.
Tip: start from a row or column that has only one '?' (Dev's row), then keep going through rows and columns in turn.
Question 2
Single correct option
What was Esha's average score across the four tests?
- A. 36
- B. 37
- C. 37.5
- D. 38
Show answer and solution
Answer: (B) 37
Esha's average is not given, but the grand total can be computed from the class averages: 5 × (37 + 38 + 40 + 37) = 760.
The other four students' totals are 160 + 152 + 156 + 144 = 612, so Esha's total = 760 − 612 = 148 and her average = 37.
Check with the completed grid: 40 + 33 + 47 + 28 = 148. ✓
The other four students' totals are 160 + 152 + 156 + 144 = 612, so Esha's total = 760 − 612 = 148 and her average = 37.
Check with the completed grid: 40 + 33 + 47 + 28 = 148. ✓
Question 3
Single correct option
How many students scored more than 40 in at least two of the four tests?
- A. 1
- B. 2
- C. 3
- D. 4
Show answer and solution
Answer: (B) 2
Completed grid:
- Aditi 42, 38, 45, 35: two scores above 40 ✓
- Bharat 30, 44, 36, 42: two ✓
- Charu 48, 40, 32, 36: one (40 is not *more than* 40)
- Dev 25, 35, 40, 44: one
- Esha 40, 33, 47, 28: one
Answer: 2.
Trap: counting a score of exactly 40 gives 4.
- Aditi 42, 38, 45, 35: two scores above 40 ✓
- Bharat 30, 44, 36, 42: two ✓
- Charu 48, 40, 32, 36: one (40 is not *more than* 40)
- Dev 25, 35, 40, 44: one
- Esha 40, 33, 47, 28: one
Answer: 2.
Trap: counting a score of exactly 40 gives 4.
Question 4
Single correct option
For the final ranking, each student's lowest test score is dropped and the other three are added. Who ranks second?
- A. Aditi
- B. Bharat
- C. Charu
- D. Esha
Show answer and solution
Answer: (C) Charu
Best-three totals (total − lowest score):
- Aditi 160 − 35 = 125
- Bharat 152 − 30 = 122
- Charu 156 − 32 = 124
- Dev 144 − 25 = 119
- Esha 148 − 28 = 120
Order: Aditi, Charu, Bharat, Esha, Dev. Charu ranks second.
- Aditi 160 − 35 = 125
- Bharat 152 − 30 = 122
- Charu 156 − 32 = 124
- Dev 144 − 25 = 119
- Esha 148 − 28 = 120
Order: Aditi, Charu, Bharat, Esha, Dev. Charu ranks second.
Question 5
Numerical answer
What is the difference between the highest and the lowest score in T2?
Show answer and solution
Answer: 11
T2 scores: Aditi 38, Bharat 44, Charu 40, Dev 35, Esha 33 (Bharat's and Charu's were deduced; see the completed grid).
Highest − lowest = 44 − 33 = 11.
Highest − lowest = 44 − 33 = 11.
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