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10 Jul 2025, 10:00
Kudos
Bookmarks
If more than 50 pages are on Lower Shelf, then is T3 on lower shelf?
Multiply all fraction by 60
T1= 11
T2=48
T3=14
T4=18
T5 =9
Total=100
(1) T2 and T4 have been placed on the lower shelf.
T2+T4=48+18=66
More than half is already on Lower Shelf
Sufficient
(2) T1 and T5 have been placed on the upper shelf.
T1+T5= 11+9=20
Any from T2, T3, T4 could be on upper or lower shelfs
Insufficient
A
Multiply all fraction by 60
T1= 11
T2=48
T3=14
T4=18
T5 =9
Total=100
(1) T2 and T4 have been placed on the lower shelf.
T2+T4=48+18=66
More than half is already on Lower Shelf
Sufficient
(2) T1 and T5 have been placed on the upper shelf.
T1+T5= 11+9=20
Any from T2, T3, T4 could be on upper or lower shelfs
Insufficient
A
10 Jul 2025, 10:03
Kudos
Bookmarks
Statement 1 alone is insufficient because we could have multiple combinations of books to receive a fraction of over 50% of total pages on the lower shelf, this is due to the fact that T2 and T4 together are 26/60, so we could add any off the other books which would be enough to fulfill the criteria.
Statement 2 alone is sufficient because we only have two possible combinations for the lower shelf to comprise more than 50% of the pages which is either T3 and T4 or T2, T3 and T4. This is due to the fact that T2 and T4 alone do not contain enough pages to fulfill the shelf requirement, thus we can answer the question sufficiently with yes T3 will be found on the lower shelf. Answer B.
Regards,
Lucas
Statement 2 alone is sufficient because we only have two possible combinations for the lower shelf to comprise more than 50% of the pages which is either T3 and T4 or T2, T3 and T4. This is due to the fact that T2 and T4 alone do not contain enough pages to fulfill the shelf requirement, thus we can answer the question sufficiently with yes T3 will be found on the lower shelf. Answer B.
Regards,
Lucas
Bunuel
kurruhee
Joined: 29 Mar 2025
Last visit: 14 Feb 2026
Posts: 36
Given Kudos: 21
Location: India
Schools: IIMA '26 (D) EPGP '26 (D) IIMC'26 (A) ISB '26 (S)
GMAT Focus 1: 575 Q78 V78 DI79 
GPA: 7.29
10 Jul 2025, 10:09
Kudos
Bookmarks
First convert all fractions to have the same denominator ie. 60.
[11][/60] [8][/60] [14][/60] [18][/60] [9][/60]
Statement (1)
Insufficient as we cannot find which other book accompanies T2 and T4 on the lower shelf. A and D are out.
Statement (2)
If T1 and T5 are on the upper shelf all the other books MUST be on the lower shelf. Sufficient. B is right.
[11][/60] [8][/60] [14][/60] [18][/60] [9][/60]
Statement (1)
Insufficient as we cannot find which other book accompanies T2 and T4 on the lower shelf. A and D are out.
Statement (2)
If T1 and T5 are on the upper shelf all the other books MUST be on the lower shelf. Sufficient. B is right.
Bunuel
10 Jul 2025, 10:18
Kudos
Bookmarks
We are given:
We know more than 1/2 of the total pages(>30/60) are on the lower shelf. Is T3 on the lower shelf?
Statement (1): T2 and T4 are on the lower shelf
T2=8/60 and T4= 18/60
Total= 26/60
So to exceed 30/60 on the lower shelf, we need more than 4/60 extra. which T1, T3 and T5 any can compensate. Therefore, we can't tell with surety for T3.
Insufficient.
Statement (2): T1 and T5 are on the upper shelf
T1=11/60 and T5=9/60
Total=9/60
Then lower shelf = remaining books = T2 + T3 + T4
= 8/60 + 14/60 + 18/60 = 40/60
This is more than 30/60, so the condition is satisfied. T3 is on the lower shelf.
Sufficient.
B) Statement 2 alone is sufficient.
- T1 = 11/60
- T2 = 2/15 = 8/60
- T3 = 7/30 = 14/60
- T4 = 3/10 = 18/60
- T5 = 3/20 = 9/60
We know more than 1/2 of the total pages(>30/60) are on the lower shelf. Is T3 on the lower shelf?
Statement (1): T2 and T4 are on the lower shelf
T2=8/60 and T4= 18/60
Total= 26/60
So to exceed 30/60 on the lower shelf, we need more than 4/60 extra. which T1, T3 and T5 any can compensate. Therefore, we can't tell with surety for T3.
Insufficient.
Statement (2): T1 and T5 are on the upper shelf
T1=11/60 and T5=9/60
Total=9/60
Then lower shelf = remaining books = T2 + T3 + T4
= 8/60 + 14/60 + 18/60 = 40/60
This is more than 30/60, so the condition is satisfied. T3 is on the lower shelf.
Sufficient.
B) Statement 2 alone is sufficient.
