Class X Board Examination Scores

CAT 2006 Slot 1 · DILR · Medium · Data Interpretation

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Passage / data set

In a Class X Board examination, ten papers are distributed over five Groups - PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan's score in English Paper II has been intentionally removed in the table.)

Name of the studentPCB Group (Phy, Chem, Bio)Mathematics GroupSocial Science Group (Hist, Geo)Vernacular Group (Paper I, Paper II)English Group (Paper I, Paper II)Final Score
Ayesha (G)98, 96, 979895, 9394, 9696, 9896.2
Ram (B)97, 99, 959795, 9694, 9496, 9896.1
Dipan (B)98, 98, 989596, 9596, 9496, ??96.0
Sagnik (B)97, 98, 999696, 9894, 9792, 9495.9
Sanjiv (B)95, 96, 979897, 9692, 9395, 9695.7
Shreya (G)96, 89, 8510097, 9894, 9596, 9595.5
Joseph (B)90, 94, 9810094, 9790, 9294, 9595.0
Agni (B)96, 99, 969995, 9682, 9392, 9394.3
Pritam (B)98, 98, 959883, 9590, 9394, 9493.9
Tirna (G)96, 98, 979985, 9492, 9187, 9693.7

Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.

Question 1 of 5

How much did Dipan get in English Paper II?

  1. A.

    94

  2. B.

    96.5

  3. C.

    97

  4. D.

    98

  5. E.

    99

Answer

97

Explanation

Dipan's Group Scores:

  • PCB = (98+98+98)/3=98(98+98+98)/3 = 98
  • Math = 9595
  • Social Science = (96+95)/2=95.5(96+95)/2 = 95.5
  • Vernacular = (96+94)/2=95(96+94)/2 = 95
  • English = (96+x)/2(96 + x)/2

Final Score = 98+95+95.5+95+(96+x)/25=96.0\frac{98 + 95 + 95.5 + 95 + (96+x)/2}{5} = 96.0 383.5+96+x2=480  ⟹  96+x2=96.5  ⟹  96+x=193  ⟹  x=97383.5 + \frac{96+x}{2} = 480 \implies \frac{96+x}{2} = 96.5 \implies 96 + x = 193 \implies x = 97.

Question 2 of 5

Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups?

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

  5. E.

    5

Answer

Option A — 1

Explanation

Checking the boys:

  • Ram: Vernacular papers are 94, 94 (neither is ≥95\ge 95). No.
  • Dipan: PCB (98), Math (95), SS (96), Vernacular (96), English (96). Yes (at least one ≥95\ge 95 in each group).
  • Sagnik: English papers are 92, 94. No.
  • Sanjiv: Vernacular papers are 92, 93. No.
  • Joseph: Vernacular papers are 90, 92. No.
  • Agni: Vernacular papers are 82, 93. No.
  • Pritam: English papers are 94, 94. No. Only Dipan satisfies the condition. Count = 1.

Question 3 of 5

Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, then their standing in decreasing order of final score would be:

  1. A.

    Pritam, Joseph, Tirna, Agni

  2. B.

    Joseph, Tirna, Agni, Pritam

  3. C.

    Pritam, Agni, Tirna, Joseph

  4. D.

    Joseph, Tirna, Pritam, Agni

  5. E.

    Pritam, Tirna, Agni, Joseph

Answer

Pritam, Joseph, Tirna, Agni

Explanation

Original SS Group Scores:

  • Pritam: (83+95)/2=89(83+95)/2 = 89. Increase to 100  ⟹  +11100 \implies +11 in Group Score   ⟹  +2.2\implies +2.2 in Final Score. New score = 93.9+2.2=96.193.9 + 2.2 = 96.1.
  • Joseph: (94+97)/2=95.5(94+97)/2 = 95.5. Increase to 100  ⟹  +4.5100 \implies +4.5 in Group Score   ⟹  +0.9\implies +0.9 in Final Score. New score = 95.0+0.9=95.995.0 + 0.9 = 95.9.
  • Tirna: (85+94)/2=89.5(85+94)/2 = 89.5. Increase to 100  ⟹  +10.5100 \implies +10.5 in Group Score   ⟹  +2.1\implies +2.1 in Final Score. New score = 93.7+2.1=95.893.7 + 2.1 = 95.8.
  • Agni: (95+96)/2=95.5(95+96)/2 = 95.5. Increase to 100  ⟹  +4.5100 \implies +4.5 in Group Score   ⟹  +0.9\implies +0.9 in Final Score. New score = 94.3+0.9=95.294.3 + 0.9 = 95.2.

Standing in decreasing order: Pritam (96.1) > Joseph (95.9) > Tirna (95.8) > Agni (95.2).

Question 4 of 5

Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:

  1. A.

    Shreya

  2. B.

    Ram

  3. C.

    Ayesha

  4. D.

    Dipan

  5. E.

    No one from the top ten

Answer

Dipan

Explanation

Checking students whose Group Scores in ALL 5 groups are ≥95\ge 95:

  • Ayesha: SS Group score = 94 (not ≥95\ge 95).
  • Ram: Vernacular Group score = 94 (not ≥95\ge 95).
  • Dipan: PCB = 98, Math = 95, SS = 95.5, Vernacular = 95, English = 96.5. All ≥95\ge 95. Dipan is eligible and gets the prize.

Question 5 of 5

Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:

  1. A.

    Ram

  2. B.

    Agni

  3. C.

    Pritam

  4. D.

    Ayesha

  5. E.

    Dipan

Answer

Dipan

Explanation

To maximize final score gain, a student should increase score in a group with fewer papers (e.g. Math with 1 paper gives +(100−x)/5+ (100 - x) / 5 increase, SS/Vern/Eng with 2 papers gives +(100−x)/10+ (100 - x) / 10 increase, PCB with 3 papers gives +(100−x)/15+ (100 - x) / 15 increase).

  • Dipan: Math is 95 (1 paper group). Increasing Math to 100 adds +5/5=+1.0+5/5 = +1.0 to Final Score   ⟹  96.0+1.0=97.0\implies 96.0 + 1.0 = 97.0.
  • Ayesha: Lowest paper in a 2-paper group is 93 in Geo. Increase adds +7/10=+0.7  ⟹  96.2+0.7=96.9+7/10 = +0.7 \implies 96.2 + 0.7 = 96.9. Dipan ends up with 97.0, which is the highest.

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