Question:easy

One-third of one fourth of a number is 12. Then the number is

Show Hint

"Of" means multiply, so one-third times one-fourth is one-twelfth. The number is therefore 12 multiplied by 12.
Updated On: Jul 17, 2026
  • 96
  • 144
  • 108
  • 36
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Undo the operations in reverse order.
The sentence describes two shrinking steps applied to the number: first take a quarter of it, then take a third of that. To get the number back, undo those steps in the opposite order, turning each division into a multiplication.

Step 2: Undo the "one-third".
A third of some quantity is 12, so that quantity is
\[ 12 \times 3 = 36 \]
This 36 is one-fourth of the number.

Step 3: Undo the "one-fourth".
A fourth of the number is 36, so the number is
\[ 36 \times 4 = 144 \]

Step 4: Confirm with a single-shot method.
Both shrink factors together divide the number by $3 \times 4 = 12$. So the number is $12$ times the given result:
\[ N = 12 \times 12 = 144 \]
The same figure appears by both routes.

Step 5: Test each option against the words.
For 96: a fourth is 24, a third of 24 is 8. Not 12.
For 144: a fourth is 36, a third of 36 is 12. This matches.
For 108: a fourth is 27, a third of 27 is 9. Not 12.
For 36: a fourth is 9, a third of 9 is 3. Not 12.
Only one option survives, so no doubt is left.

Step 6: The lesson.
When a question chains "of" statements, multiply all the fractions together first and treat the whole chain as one factor. It removes the chance of applying only one of the two fractions, which is the mistake that produces 36 and 108 here.

Final Answer:
The number asked for is 144.
\[ \boxed{144} \]
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