One chocolate bar is divided into two equal halves... | Free GMAT Practice Question | GMAT Panda

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Question

One chocolate bar is divided into two equal halves. One half is then divided into 5 equal pieces and the other half into 7 equal pieces. If someone eats 2 of the pieces from the half cut into 5 pieces and 3 of the pieces from the half cut into 7 pieces, what fraction of the original chocolate bar remains?

Answer Choices

A. $\frac{29}{70}$
B. $\frac{41}{70}$
C. $\frac{37}{70}$
D. $\frac{39}{70}$
E. $\frac{43}{70}$

Steps

Explanation	Calculations	Help
$We use X to represent the whole chocolate bar.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We interpret "One half is then divided into 5 equal pieces" as splitting half the chocolate bar into 5 equal parts to find the size of one such piece.$	$\frac{1}{2} X \times \frac{1}{5} = \frac{1}{10} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We interpret "the other half is then divided into 7 equal pieces" as splitting the remaining half into 7 equal parts to find the size of one such piece.$	$\frac{1}{2} X \times \frac{1}{7} = \frac{1}{14} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eats 2 of the pieces from the half cut into 5 pieces and 3 of the pieces from the half cut into 7 pieces" into the sum of the amounts eaten.$	$2 \times \frac{1}{10} X + 3 \times \frac{1}{14} X = \frac{2}{10} X + \frac{3}{14} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We simplify the fraction of the half-5-pieces eaten by canceling common factors.$	$\frac{2}{10} X = \frac{2}{2 \times 5} X = \frac{1}{5} X$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We convert to a common denominator and add the eaten portions.$	$\frac{1}{5} X = \frac{14}{70} X \frac{3}{14} X = \frac{15}{70} X \frac{14}{70} X + \frac{15}{70} X = \frac{29}{70} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole chocolate bar.$	$X - \frac{29}{70} X = \frac{70}{70} X - \frac{29}{70} X = \frac{41}{70} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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Final Answer

B

Question

One chocolate bar is divided into two equal halves. One half is then divided into 5 equal pieces and the other half into 7 equal pieces. If someone eats 2 of the pieces from the half cut into 5 pieces and 3 of the pieces from the half cut into 7 pieces, what fraction of the original chocolate bar remains?

Answer Choices

A. $\frac{29}{70}$
B. $\frac{41}{70}$
C. $\frac{37}{70}$
D. $\frac{39}{70}$
E. $\frac{43}{70}$

Steps

Explanation	Calculations	Help
$We use X to represent the whole chocolate bar.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We interpret "One half is then divided into 5 equal pieces" as splitting half the chocolate bar into 5 equal parts to find the size of one such piece.$	$\frac{1}{2} X \times \frac{1}{5} = \frac{1}{10} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We interpret "the other half is then divided into 7 equal pieces" as splitting the remaining half into 7 equal parts to find the size of one such piece.$	$\frac{1}{2} X \times \frac{1}{7} = \frac{1}{14} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eats 2 of the pieces from the half cut into 5 pieces and 3 of the pieces from the half cut into 7 pieces" into the sum of the amounts eaten.$	$2 \times \frac{1}{10} X + 3 \times \frac{1}{14} X = \frac{2}{10} X + \frac{3}{14} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We simplify the fraction of the half-5-pieces eaten by canceling common factors.$	$\frac{2}{10} X = \frac{2}{2 \times 5} X = \frac{1}{5} X$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We convert to a common denominator and add the eaten portions.$	$\frac{1}{5} X = \frac{14}{70} X \frac{3}{14} X = \frac{15}{70} X \frac{14}{70} X + \frac{15}{70} X = \frac{29}{70} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole chocolate bar.$	$X - \frac{29}{70} X = \frac{70}{70} X - \frac{29}{70} X = \frac{41}{70} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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Final Answer

B