The task is to work out whether: 1. One or both of the statements alone is/are…

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The task is to work out whether:

1. One or both of the statements alone is/are sufficient for the question to be answered

2. The statements in isolation are useless but together they can solve the problem

3. Neither statement is of any use and the problem cannot be solved

The list of answer options are presented from A to E and are always the same.

A supermarket chain agreed to donate 'x' dollars to a homeless charity for every loaf of bread its stores sold during a Help the Homeless week. What was the total amount expected to be donated?

(1) A total of 5,000 loaves were expected to be sold

(2) 120 more loaves were sold than expected, so the total amount actually donated was $2,500

  1. A.

    Statement 1 alone is sufficient, but statement 2 alone is not sufficient

  2. B.

    Statement 2 alone is sufficient, but statement 1 alone is not sufficient

  3. C.

    Both statements together are sufficient, but neither statement alone is sufficient

  4. D.

    Each statement alone is sufficient

  5. E.

    Statements 1 and 2 together are not sufficient

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Data Sufficiency asks only whether the given statements pin the target quantity down to one unique value, not what that value is. A statement, or a combination of statements, is sufficient exactly when it leaves exactly one unknown in a solvable equation for what is asked; if any unknown remains free, the value cannot be fixed and the statement is insufficient.

  1. Statement (1) alone: the expected loaf count is fixed at 5,000, so the expected total donation is 5,000 times 'x'. But the per-loaf donation rate 'x' has no value assigned anywhere in this statement, so the total cannot be reduced to one number. Statement (1) alone is insufficient.

  2. Statement (2) alone: 120 more loaves than expected were sold, and the actual amount donated for all loaves sold was $2,500, giving (expected loaves + 120) times 'x' equals $2,500. This single equation has two unknowns, the expected loaf count and the rate 'x', so it cannot be solved for either on its own. Statement (2) alone is insufficient.

  3. Combining both: statement (1) fixes the expected loaf count at 5,000, so the loaves actually sold were 5,000 + 120 = 5,120. Substituting into statement (2)'s relationship gives 5,120 times 'x' equals $2,500, now a single equation in the single unknown 'x', which is solvable in principle. Since 'x' is pinned to one value, the expected total donation, 5,000 times 'x', is also pinned to one value.

Confirm no shortcut exists: expressing 'x' as 2,500 divided by 5,120 and substituting back into 5,120 times 'x' reproduces exactly $2,500, verifying the equation is internally consistent and genuinely solvable with both statements, and that neither statement supplies enough on its own, since each is missing one of the two needed quantities, the loaf count or the rate.

Since only the combination of both statements reduces the problem to one equation in one unknown, both statements together are sufficient, while neither is sufficient alone.

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