Five children sat for an aptitude test. In the result report, it was noted that child A scored less marks than child B. Child C scored less marks than child D. Child B scored less marks than child C and child A scored more marks than the child E. Who did score the highest marks?
D
Aptitude Test Score Comparison Problem
This problem requires us to determine the highest score among five children based on the given relational statements about their scores. We will deduce the order of scores by combining the provided information.
Analyzing the Given Score Relationships
Let's represent the scores of the five children A, B, C, D, and E. We are given the following comparisons:
- Child A scored less marks than child B. Mathematically, this is \(\text{Score}(A) < \text{Score}(B)\).
- Child C scored less marks than child D. Mathematically, this is \(\text{Score}(C) < \text{Score}(D)\).
- Child B scored less marks than child C. Mathematically, this is \(\text{Score}(B) < \text{Score}(C)\).
- Child A scored more marks than child E. Mathematically, this is \(\text{Score}(A) > \text{Score}(E)\), or \(\text{Score}(E) < \text{Score}(A)\).
Combining the Score Inequalities
Now, let's chain these inequalities together to establish a complete or partial order of the children's scores.
- We know \(\text{Score}(A) < \text{Score}(B)\) and \(\text{Score}(B) < \text{Score}(C)\). Combining these gives us \(\text{Score}(A) < \text{Score}(B) < \text{Score}(C)\).
- Next, we have \(\text{Score}(B) < \text{Score}(C)\) and \(\text{Score}(C) < \text{Score}(D)\). Combining these extends the chain: \(\text{Score}(B) < \text{Score}(C) < \text{Score}(D)\).
- Putting the results from step 1 and step 2 together, we get a clear order for children A, B, C, and D: \(\text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\).
- Finally, we have the relationship \(\text{Score}(E) < \text{Score}(A)\). Since A's score is already established as the lowest among A, B, C, and D in the chain \(\text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\), and E scored even less than A, E's score is the lowest of all five children.
The complete order of scores from lowest to highest is \(\text{Score}(E) < \text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\).
Identifying the Highest Score
From the combined inequality \(\text{Score}(E) < \text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\), it is clear that Child D has the highest score among the five children.
| Statement | Inequality |
|---|---|
| A scored less than B | A < B |
| C scored less than D | C < D |
| B scored less than C | B < C |
| A scored more than E | E < A |
Conclusion on Highest Score
Based on the step-by-step deduction of the score relationships, Child D scored the highest marks in the aptitude test.
Revision Table: Aptitude Test Score Comparison
| Step | Description |
|---|---|
| 1 | List all given relationships (e.g., inequalities). |
| 2 | Combine relationships to form longer chains or establish direct comparisons. |
| 3 | Identify the highest or lowest element based on the final combined order. |
Additional Information: Logical Deduction and Ranking
Problems like this one are common in aptitude tests and involve logical deduction. They require you to piece together several pieces of information to arrive at a conclusion about the relative positions (ranking) of items or individuals. These questions test your ability to follow logical steps and manage multiple constraints simultaneously. Practicing such problems helps improve analytical and reasoning skills.
- Logical Deduction: Using given premises to infer a conclusion that must be true if the premises are true.
- Ranking Problems: Arranging elements in a specific order based on given comparisons (e.g., height, weight, scores).
- Transitivity: The principle used here (if A < B and B < C, then A < C) is called transitivity.
Being systematic in listing and combining the given facts is crucial for solving these logical deduction problems accurately.
Similar Questions
Horse E was running ahead of horse D in the middle of the race. Horse C was ahead of horse A but behind horse B. Horse A was running ahead of horse E. From this point on, the fourth-placed horse took the lead and won the race. If the positions of the other horses remained the same, which horse was in the middle at the end of the race?
Ina class of 64 students, Komal’s rank is 6 positions lower (i.e. towards bottom) than her friend Shikha, who is at the 59 th position from the end. What is Komal’s rank from the top in the class?
In a shopping mall, five water bottles labelled as A, B, C, D and E were placed in a rack.
The bottle A has less price than the bottle B. The bottle C has less price than the bottle D. The bottle B has less price than the bottle C and bottle A has more price than the bottle E.
If a customer wants to buy a bottle of maximum price, then which bottle he/she has to buy?In a class, there are 40 students. Some of them passed the examination and others failed. Raman’s rank among the student who have passed is 13 th from top and 17th from bottom. How many students have failed?
- D, E, K, W, X, Y and Z scored different marks in an exam. K scored more than only two people. E scored less than only one person. W scored more than D but less than both E and Z. D did not score the lowest marks and Z did not score the highest marks. X scored less than Y. How many people scored more than Y?
Rohan is 13 th from top and Raman is 36 th from bottom in the list of passed students. There are 5 students between Raman and Rohan. 9 students failed. How many minimum students are there?
In a silk sari showroom there are 10 exclusive and highly expensive saris- 3 of Kalamkari, 3 Ikat, 2 Kanchi and 2 Banaras, are arranged in a shelf from top to bottom as follows;
There is a Banaras sari between a Kalamkari and Kanchi sari,
A Kalamkari sari between a Kanchi and an Banaras sari.
A Ikat sari between a Banaras and a Kanchi sari,
A Kanchi sari between two Ikat saris and
Two Ikat saris between a Kanchi and a Kalamkari sari.
Which type of sari is present in that arrangement in 6th place from top?
In a class, five children wrote the aptitude test.
In the result report, it was noted that the child A got less marks than the child B. The child C got less marks than the child D. The child B is got less mark than the child C and child A got more marks than the child E. Which child got the second-highest marks?Weight of P is twice that of Q. Weight of Q is half of R. Weight of R is 3 times of T. Weight of T is half of S. The weight of Q is greater than the weight of how many persons among P, R, S and T?
In a row Sanjay is at 11 th position from top and 13 th from bottom. How many people are there in the row?
Important Questions from Ordering and Ranking
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled on Monday?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled between Statistics and English?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is the last one in the week?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled on Wednesday?
In a row 'A' is in the 11th position from the left and 'B' is in the 10th position from the right. If 'A' and 'B' interchange, then 'A' becomes 18th from the left.
How many persons are there in the row other than 'A' and 'B'?
