Comprehension

Arjun bought seven grocery items A, B, C, D, E, F, and G each having a different weight. Item D is heavier than only three items but lighter than exactly three items. Item G is lighter than A but heavier than B and C. The second lightest item weighs exactly half of the heaviest item. Item F is neither the heaviest nor the second heaviest. Item C is the lightest among all. Item A weighs 18 kg and is not the heaviest. Number of items heavier than E is one less than the number items lighter than F.

What is the possible weight of E?

  1. 11 kg
  2. 21 kg
  3. 17.5 kg
  4. 15 kg
  5. 6 kg

Answer (Detailed Solution Below)

Option 2 : 21 kg

Detailed Solution

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Given: Arjun bought seven grocery items A, B, C, D, E, F, and G each having a different weight. 

1) Item D is heavier than only three items but lighter than exactly three items. 

2) Item C is the lightest among all. 

_ > _ > _ > D > _ > _ > C

3) Item G is lighter than A but heavier than B and C. 

4) A weighs 18 kg and is not the heaviest. 

Case 1) _ > A (18 kg) > G > D > B > _ > C

Case 2) _ > A (18 kg) > _ > D > G > B > C

Case 3) _ > _ > A (18 kg) > D > G > B > C

5) Item F is neither the heaviest nor the second heaviest.

As there is no possible position for F in case 3, therefore it is eliminated.

After positioning F only one position is left which will be occupied by the only item left i.e. E.

Case 1) E > A (18 kg) > G > D > B > F > C

Case 2) E > A (18 kg) > F > D > G > B > C

6) Number of items heavier than E is one less than the number items lighter than F.

As case 2 doesn't fulfil the condition, therefore is eliminated.

In case 1 → Number of items heavier than E is = 0 and Number of items lighter than F is = 1, thus condition is justified here.

Case 1) E > A (18 kg) > G > D > B > F > C

Thus, according to the final arrangement, as E is heavier than A, therefore E's weight will be higher than 18 kg.

∴ E' weight is 21 kg.

Hence, "Option 2" is the correct answer.

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