What is the maximum number of students among whom all 1001 pens and all 910 pencils can be distributed,…
The number of students must divide both 1001 and 910 exactly. Their greatest common divisor is 91, since 1001 − 910 = 91 and 910 = 10 × 91. Thus 91 students can each receive…
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What is the maximum number of students among whom all 1001 pens and all 910 pencils can be distributed, with every student receiving the same positive whole number of pens and the same positive whole number of pencils?
Answer and explanation
Correct answer A
The number of students must divide both 1001 and 910 exactly. Their greatest common divisor is 91, since 1001 − 910 = 91 and 910 = 10 × 91. Thus 91 students can each receive 11 pens and 10 pencils.
Option feedback
Option A
91 divides both quantities, giving 11 pens and 10 pencils each.
Option B
910 does not divide 1001.
Option C
1001 does not divide 910 and exceeds the pencil count.
Option D
1911 exceeds each item count and cannot give each student a positive whole number of both.
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Gujarat Judicial Services