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01 Jul 2026, 19:00
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E
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Difficulty:
95%
(hard)
Question Stats:
30% (02:26) correct
70%
(02:51)
wrong
based on 86
sessions
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Time
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Not Attempted Yet
At the end of Monday, a bookstore display had only hardcover books and paperback books, and 7/12 of the books on the display were hardcovers. On Tuesday, the store added hardcover books and paperback books to the display and removed none of the books that were already there. After the additions, was the fraction of paperback books on the display less than it had been at the end of Monday?
(1) Less than 1/2 of the books added on Tuesday were paperbacks.
(2) After the additions on Tuesday, the total number of books on the display was 1/3 greater than it had been at the end of Monday.
(1) Less than 1/2 of the books added on Tuesday were paperbacks.
(2) After the additions on Tuesday, the total number of books on the display was 1/3 greater than it had been at the end of Monday.
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M47-224
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
01 Jul 2026, 23:32
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say monday total books = 60x
hardcover= 35x
paperback = 25x
tuesday, added hardcover = m
paperback = n
no books were removed.
so total book on tuesday = 60x+m+n
hardcover= 35x+m
paperback= 25x+ n
find: 25x+n/ 60x+m+n < 25x/60x
25x+n / 60x+m+n < 5/12
300x+12n < 300x+5m+5n
12n < 5m+5n
7n< 5m
this is what we need to find.
S-1
total books added on tuesday = m+n
paperback = n
paperback < (1/2) (m+n)
n < (1/2) (m+n)
2n < m+n
n<m
here with different values we get both yes and no for our inequality.
so not sufficient.
S-2
total books added on tuesday= m+n
60x+m+n = (4/3) (60x)
60x+m+n = 80x
m+n = 20x
now, we can try two extreme cases here.
C-1 m = 19x, n= x
in this case 7n< 5m holds true.
C-s, m=x, n=19x
in this case 7n< 5m doesnt hold true.
not sufficient
S- 1&2
we know n<m and m+n = 20x
again we can try two cases.
n= 5, m= 15, then 7n< 5m holds true.
n=9, m=11, then 7n< 5m doesnt hold true.
choice E
hardcover= 35x
paperback = 25x
tuesday, added hardcover = m
paperback = n
no books were removed.
so total book on tuesday = 60x+m+n
hardcover= 35x+m
paperback= 25x+ n
find: 25x+n/ 60x+m+n < 25x/60x
25x+n / 60x+m+n < 5/12
300x+12n < 300x+5m+5n
12n < 5m+5n
7n< 5m
this is what we need to find.
S-1
total books added on tuesday = m+n
paperback = n
paperback < (1/2) (m+n)
n < (1/2) (m+n)
2n < m+n
n<m
here with different values we get both yes and no for our inequality.
so not sufficient.
S-2
total books added on tuesday= m+n
60x+m+n = (4/3) (60x)
60x+m+n = 80x
m+n = 20x
now, we can try two extreme cases here.
C-1 m = 19x, n= x
in this case 7n< 5m holds true.
C-s, m=x, n=19x
in this case 7n< 5m doesnt hold true.
not sufficient
S- 1&2
we know n<m and m+n = 20x
again we can try two cases.
n= 5, m= 15, then 7n< 5m holds true.
n=9, m=11, then 7n< 5m doesnt hold true.
choice E
Bunuel
01 Jul 2026, 23:33
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Bookmarks
Let Monday total = 12k.
Hardcovers = 7k, Paperbacks = 5k.
Let Tuesday additions be H and P.
Need to know if
{5k+P}/{12k+H+P} < {5}/{12}
This simplifies to: 12P < 5(H + P) = 7P < 5H.
(1) Less than half the added books were paperbacks:
P < (H + P)/2
2P < H + P
P < H
This does not guarantee 7P < 5H.
Not sufficient.
(2) Tuesday total is 1/3 greater:
H + P = 4k.
No information about H vs. P.
Not sufficient.
Together: H + P = 4k and P < 2k.
Need 7P < 5H = 5(4k − P):
12P < 20k
P < 5k/3.
Since P < 2k, both P < 5k/3 and P > 5k/3 are possible.
Cannot determine.
Answer: E
Hardcovers = 7k, Paperbacks = 5k.
Let Tuesday additions be H and P.
Need to know if
{5k+P}/{12k+H+P} < {5}/{12}
This simplifies to: 12P < 5(H + P) = 7P < 5H.
(1) Less than half the added books were paperbacks:
P < (H + P)/2
2P < H + P
P < H
This does not guarantee 7P < 5H.
Not sufficient.
(2) Tuesday total is 1/3 greater:
H + P = 4k.
No information about H vs. P.
Not sufficient.
Together: H + P = 4k and P < 2k.
Need 7P < 5H = 5(4k − P):
12P < 20k
P < 5k/3.
Since P < 2k, both P < 5k/3 and P > 5k/3 are possible.
Cannot determine.
Answer: E
