Eli has arranged all his books on two shelves such that the upper and

Question

Eli has arranged all his books on two shelves such that the upper and lower shelves each hold the same number of books. Exactly half of the books in the collection are children’s books, all of which have illustrations. All the children’s books have illustrations only on the right (IOR)—that is, on odd-numbered pages only. Do the majority of the books on the lower shelf have IOR?

(1) A majority of the children’s books are on the lower shelf.

(2) A majority of the books that have IOR are on the upper shelf.

(1) A majority of the children’s books are on the lower shelf.

(2) A majority of the books that have IOR are on the upper shelf.

Bunuel · Accepted Answer

Eli has arranged all his books on two shelves such that the upper and lower shelves each hold the same number of books. Exactly half of the books in the collection are children’s books, all of which have illustrations. All the children’s books have illustrations only on the right (IOR)—that is, on odd-numbered pages only. Do the majority of the books on the lower shelf have IOR?

(1) A majority of the children’s books are on the lower shelf.

(2) A majority of the books that have IOR are on the upper shelf.

Assuming the total number of books is 16, the number of children’s books, all with IOR, is 8. Each shelf holds 8 books, and we need to find out whether more than 4 books on the lower shelf have IOR.

(1) A majority of the children’s books are on the lower shelf.

This implies that 5 or more children’s books are on the lower shelf. Since all of them have IOR and there are 8 books on the lower shelf, a majority of the books on the lower shelf have IOR. Sufficient.

(2) A majority of the books that have IOR are on the upper shelf.

If only children’s books (8) have IOR and all of them are on the upper shelf, then no book on the lower shelf will have IOR and the answer to the question would be NO. However, if 11 books have IOR and 6 of them are on the upper shelf, that still leaves 5 books with IOR on the lower shelf, and in this case the answer would be YES. Not sufficient.

Answer: A.

Archit3110 · Answer

given that there are two shelves with equal number of books on each

Fact : Exactly half of the books in the collection are children’s books, all of which have illustrations

Fact 2: All the children’s books have illustrations only on the right (IOR)—that is, on odd-numbered pages only.

Target :
Do the majority of the books on the lower shelf have IOR?

#1
1) A majority of the children’s books are on the lower shelf.
sufficient as fact 1 & fact 2 are matching sufficient
#2
A majority of the books that have IOR are on the upper shelf.
there is no clarity that the books which are on upper shelf are all children books are others as there is no restriction of non children books having IOR ... 
insufficeint

OPTION A

bhanu29 · Answer

MartyMurray   KarishmaB  would love to hear your analysis.

MartyMurray · Answer

Eli has arranged all his books on two shelves such that the upper and lower shelves each hold the same number of books. Exactly half of the books in the collection are children’s books, all of which have illustrations. All the children’s books have illustrations only on the right (IOR)—that is, on odd-numbered pages only. Do the majority of the books on the lower shelf have IOR?

(1) A majority of the children’s books are on the lower shelf.

(2) A majority of the books that have IOR are on the upper shelf.

Given information:

Each of the two shelves holds the same number of books, meaning that each shelf holds 1/2 of the books.

1/2 of the books in the collection are children's books.

All of the children's books have IOR, meaning that AT LEAST 1/2 of the books have IOR.

(1) A majority of the children’s books are on the lower shelf.

Since 1/2 of the books are children's books, a majority of the children's books is more than 1/4 of all the books.

The lower shelf holds 1/2 of all the books.

More than 1/4 of all the books is the majority of 1/2 of all the books.

So, a majority of the children's books would also be the majority of books on the lower shelf.

So, since children's books all have IOR, this statement confirms that the majority of the books on the lower shelf have IOR.

Sufficient.

(2) A majority of the books that have IOR are on the upper shelf.

The passage indicates only that all children's books have IOR. It does not indicate what fraction of the other books have IOR. So, it could be that only the children's books have IOR or that many of the other books have IOR as well.

If only the children's books have IOR, given what this statement says, the majority of the books on the lower shelf would not have IOR. After all, if the majority of the children's books are on the upper shelf, then under 1/2 of the children's books would be on the lower shelf, constituting under 1/2 of the books on the lower shelf.

Alternatively, if many of the books other than children's books have IOR, the majority of the books with IOR could be on the upper shelf, and there could still be enough books with IOR to make up the majority of the books on the lower shelf.

So, given what this statement says, the majority of books on the lower shelf may or may not have IOR.

Insufficient.

Correct answer:   A

Eli has arranged all his books on two shelves such that the upper and

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Eli has arranged all his books on two shelves such that the upper and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards