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11 Jul 2025, 02:55
Kudos
Bookmarks
1.T2 = 8/60
T4 = 18/60
total = 26/60 < 30/60
books left= T1(11/60), T3 (14/60), T5 (9/60)
T1=26+11=37>30
T2=26+14=40>30
T3=26+9=35>30
So any of the book works.
Insufficient
2.T1 = 11/60
T5 = 9/60
Total=20/60
lower-shelf=40/60 which is greaten than 30/60
Since T1 is on the upper shelf we are left with T2,T3,T4
T2=8/60,T4=18/60
T3 would be 40-26=14
Sufficient
IMO:B
T4 = 18/60
total = 26/60 < 30/60
books left= T1(11/60), T3 (14/60), T5 (9/60)
T1=26+11=37>30
T2=26+14=40>30
T3=26+9=35>30
So any of the book works.
Insufficient
2.T1 = 11/60
T5 = 9/60
Total=20/60
lower-shelf=40/60 which is greaten than 30/60
Since T1 is on the upper shelf we are left with T2,T3,T4
T2=8/60,T4=18/60
T3 would be 40-26=14
Sufficient
IMO:B
11 Jul 2025, 03:45
Kudos
Bookmarks
T1=11/60
T2=2/15=8/60
T3=7/30=14/60
T4=3/10=18/60
T5=3/20=9/60
lower shelf > 30/60
T3 in lower shelf?
(1)
T2+T4=24/60
If lower shelf = T2, T4, T3 (38/60) the answer is yes
If lower shelf = T2, T4, T1 (35/60) the answer is no
INSUFFICIENT
(2)
T1+T5=20/60
T3 must be in the lower shelf because the other two T2, T4 are 26/60 < 30/60
lower shelf can be T3, T4 (32/60) or T2, T3, T4 (40/60)
SUFFICIENT
IMO B
T2=2/15=8/60
T3=7/30=14/60
T4=3/10=18/60
T5=3/20=9/60
lower shelf > 30/60
T3 in lower shelf?
(1)
T2+T4=24/60
If lower shelf = T2, T4, T3 (38/60) the answer is yes
If lower shelf = T2, T4, T1 (35/60) the answer is no
INSUFFICIENT
(2)
T1+T5=20/60
T3 must be in the lower shelf because the other two T2, T4 are 26/60 < 30/60
lower shelf can be T3, T4 (32/60) or T2, T3, T4 (40/60)
SUFFICIENT
IMO B
11 Jul 2025, 04:22
Kudos
Bookmarks
Given,
Five mathematics textbooks, T1, T2, T3, T4, and T5, have been placed on two shelves, neither of which houses any other books.
The table displays the number of pages in each book as a fraction of the total number of pages in the five books together.
To find:
If more than 1/2 of the total pages that comprise the five books are found on the lower shelf, is T3 found on the lower shelf?
Statement 1:
T2 and T4 have been placed on the lower shelf.
T 2 + T 4 = 8/60 + 18/60
= 26/60 < 1/2
We have no information about any other book where it can be kept.
Not Sufficient
Statement 2:
T1 and T5 have been placed on the upper shelf.
T 1 + T 5
= 11/60 + 9/60
= 20 /60
Lower shelf = 40/60 >1/2
Book on lower shelf = T2, T3, T4
Sufficient
Ans: B
Five mathematics textbooks, T1, T2, T3, T4, and T5, have been placed on two shelves, neither of which houses any other books.
The table displays the number of pages in each book as a fraction of the total number of pages in the five books together.
Textbook | T1 | T2 | T3 | T4 | T5 |
Fraction of the total pages in the five textbooks | 11/60 | 2/15 | 7/30 | 3/10 | 3/20 |
The same fraction with common denominator | 11/60 | 8/60 | 14/60 | 18/60 | 9/60 |
To find:
If more than 1/2 of the total pages that comprise the five books are found on the lower shelf, is T3 found on the lower shelf?
Statement 1:
T2 and T4 have been placed on the lower shelf.
T 2 + T 4 = 8/60 + 18/60
= 26/60 < 1/2
We have no information about any other book where it can be kept.
Not Sufficient
Statement 2:
T1 and T5 have been placed on the upper shelf.
T 1 + T 5
= 11/60 + 9/60
= 20 /60
Lower shelf = 40/60 >1/2
Book on lower shelf = T2, T3, T4
Sufficient
Ans: B
Bunuel
11 Jul 2025, 04:41
Kudos
Bookmarks
Five mathematics textbooks, T1, T2, T3, T4, and T5
2 shelves with only these 5 books
The number of pages in each book is a fraction of the total number of pages in the five books together
More than 1/2 of the total pages that comprise the five books are found on the lower shelf
We know that each book is a fraction of the total pages, so lets bring them in order
T1 = 11/60 = 11/60
T2 = 2/15 = 8/60
T3 = 7/30 = 14/60
T4 = 3/10 = 18/60
T5 = 3/20 = 9/60
So, we need to find out if T3 is on the lower shelf, given that more than 1/2 of the total page count is on the lower shelf
Given the statements,
(1) T2 and T4 have been placed on the lower shelf.
=> Lower shelf = T2 + T4 = 8/60 + 18/60 = 26/60
We know that lower shelf has more than half the page count
So lower shelf > 30/60
To satisfy this,
T1, T3 and T5 any of them can be in lower shelf to satisfy the condition i.e,
T1 + Lower shelf = 11/60 + 26/60 = 37/60 > 30/60
T3 + Lower shelf = 14/60 + 26/60 = 40/60 > 30/60
T5 + Lower shelf = 9/60 + 26/60 = 35/60 > 30/60
We cant know if T3 is on the lower shelf,
Statement (1) is insufficient
(2) T1 and T5 have been placed on the upper shelf.
=> Upper shelf = T1 + T5 = 11/60 + 9/60 = 20/60
We know that lower shelf has more than half the pages (>30/60) and we have T2, T4 and T3 as the possibilities to be in the lower shelf
T2 = 8/60 , T3 = 14/60 , T4= 18/60
Only 2 combinations for the below shelf is possible to have more than half the pages (>30/60)
T2+T3+T4 = (8+14+18)/60 = 40/60 > 30/60
T3+T4 = (14+18)/60 = 32/60 > 30/60
In both these combinations T3 is in the lower shelf
=> Statement (2) is sufficient
(B) Statement (2) alone is sufficient, but Statement (1) is not
2 shelves with only these 5 books
The number of pages in each book is a fraction of the total number of pages in the five books together
More than 1/2 of the total pages that comprise the five books are found on the lower shelf
We know that each book is a fraction of the total pages, so lets bring them in order
T1 = 11/60 = 11/60
T2 = 2/15 = 8/60
T3 = 7/30 = 14/60
T4 = 3/10 = 18/60
T5 = 3/20 = 9/60
So, we need to find out if T3 is on the lower shelf, given that more than 1/2 of the total page count is on the lower shelf
Given the statements,
(1) T2 and T4 have been placed on the lower shelf.
=> Lower shelf = T2 + T4 = 8/60 + 18/60 = 26/60
We know that lower shelf has more than half the page count
So lower shelf > 30/60
To satisfy this,
T1, T3 and T5 any of them can be in lower shelf to satisfy the condition i.e,
T1 + Lower shelf = 11/60 + 26/60 = 37/60 > 30/60
T3 + Lower shelf = 14/60 + 26/60 = 40/60 > 30/60
T5 + Lower shelf = 9/60 + 26/60 = 35/60 > 30/60
We cant know if T3 is on the lower shelf,
Statement (1) is insufficient
(2) T1 and T5 have been placed on the upper shelf.
=> Upper shelf = T1 + T5 = 11/60 + 9/60 = 20/60
We know that lower shelf has more than half the pages (>30/60) and we have T2, T4 and T3 as the possibilities to be in the lower shelf
T2 = 8/60 , T3 = 14/60 , T4= 18/60
Only 2 combinations for the below shelf is possible to have more than half the pages (>30/60)
T2+T3+T4 = (8+14+18)/60 = 40/60 > 30/60
T3+T4 = (14+18)/60 = 32/60 > 30/60
In both these combinations T3 is in the lower shelf
=> Statement (2) is sufficient
(B) Statement (2) alone is sufficient, but Statement (1) is not
