Directions : Each of the questions below consists of a question and two…

2017

Directions : Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer accordingly :

Six boxes A, B, C, D, E, F of different colours are placed one above another. Also, each box has different number of toffees. No box has same number of toffees. Only two boxes are placed in between B and Green box. No box is placed above B. Box D is placed immediately above Blue box. Only Red box is placed in between Green box and A. Only one box is placed between Red and Blue box. Only one box is placed in between D and E. Only one box is placed between Orange box and C. Box C is not of Red colour. How many number of toffees does Blue box have?
(I) Box E has more number of toffees than 8 while box C has more number of toffees than 20. Box D has 21 toffees. The box which has lowest and 2nd lowest number of toffees has 10 and 12 toffees respectively. Box A, C, D and F has odd number of toffees.
(II) A has more number of toffees than B but not more than D. The difference in the number of toffees in box F and E is 7. The box which has highest number of toffees has 8 more toffees than box F. Total number of toffees in box B and A is 31.

  1. A.

    if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

  2. B.

    if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

  3. C.

    if the data either in statement I alone or in statement II alone are sufficient to answer the question.

  4. D.

    if the data even in both statements I and II together are not sufficient to answer the question.

  5. E.

    if the data in both statements I and II together are necessary to answer the question.

Attempted by 1 students.

Show answer & explanation

Correct answer: E

Concept

In a Data Sufficiency question you must judge EACH statement on its own and then, only if needed, both together. A statement is sufficient only when it forces a single, unique answer to the asked quantity. The drill: first fix the arrangement from the puzzle clues, identify which box is being asked about, then test whether Statement I alone, Statement II alone, or only the two combined pin its value to one number.

Step 1 - Fix the arrangement (top to bottom)

No box is above B, so B is at the top. Working through the colour and gap clues (two boxes between B and Green; D immediately above Blue; only Red between Green and A; one box between Red and Blue; one box between D and E; one box between Orange and C; C is not Red) yields a single stack:

  1. B - Orange (top)

  2. D

  3. C - Blue

  4. E - Green

  5. F - Red

  6. A (bottom)

So the Blue box is C. The question reduces to: how many toffees does box C hold?

Step 2 - Test Statement I alone

Statement I gives D = 21; C is odd and greater than 20; the lowest and 2nd-lowest counts are 10 and 12; and A, C, D, F are odd. Since 10 and 12 are even, they must be the only boxes that can be even (B and E). That leaves C as any odd number above 20 other than 21 (23, 25, 27, ...). The value of C is not pinned to one number, so Statement I alone is NOT sufficient.

Step 3 - Test Statement II alone

Statement II gives A > B, A is not more than D, |F - E| = 7, the highest box has 8 more than F, and B + A = 31. None of these references box C or fixes its absolute count, so C stays undetermined. Statement II alone is NOT sufficient.

Step 4 - Combine both statements

  1. From I, the two even boxes B and E are 10 and 12. From II, B + A = 31, so A = 31 - B is 21 or 19; A = 21 clashes with D = 21, so A = 19 and B = 12, forcing E = 10.

  2. From II, |F - E| = 7 gives F = 17 or F = 3; F must exceed 12 (10 and 12 are the two lowest), so F = 17.

  3. From II, the highest count = F + 8 = 25. The known values are B = 12, E = 10, A = 19, D = 21, F = 17, so the maximum must come from C. C is odd and above 20, and the maximum is fixed at 25, hence C = 25.

Cross-check

Counts B = 12, E = 10, A = 19, D = 21, F = 17, C = 25 are all distinct; the two lowest are 10 and 12; A, C, D, F are odd; A = 19 > B = 12 and A = 19 < D = 21; B + A = 31; |F - E| = 7; and the highest (25) = F + 8. Every clue holds and C = 25 is forced only by using both statements.

Result

Each statement alone leaves the Blue box (C) undetermined, but together they fix it at 25 toffees. So both statements together are necessary to answer the question.

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