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Difficulty:
55%
(hard)
Question Stats:
70% (02:16) correct
30%
(02:16)
wrong
based on 747
sessions
History
Date
Time
Result
Not Attempted Yet
If the Celsius temperature of Object X is C and the equivalent Fahrenheit temperature of Object X is F, then \(F = \frac{9}{5}C + 32\). Is the Celsius temperature of Object X greater than 50 ?
(1) F > 120
(2) F - C > 72
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
2024-01-24_15-06-24.png [ 29.8 KiB | Viewed 8686 times ]
(1) F > 120
(2) F - C > 72
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
Attachment:
2024-01-24_15-06-24.png [ 29.8 KiB | Viewed 8686 times ]
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gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 09 Sep 2026
Posts: 3,174
Location: India
Concentration: Strategy, Leadership
Posts: 3,174
guddo
Given: F = \(\frac{9}{5}\)C + 32
Statement 1
(1) F > 120
F = \(\frac{9}{5}\)C + 32
\(\frac{9}{5}\)C + 32 > 120
\(\frac{9}{5}\)C > 88
C > \(\frac{88*9}{5}\)
Had the numerator been 90, the inequality would have been C > \(\frac{90*9}{5}\). In that case, C would have been greater than 50.
However, in this case, \( C > 49.XX\)
This statement alone is not sufficient to conclude whether C > 50. If C = 49.99, the answer to the question "Is the Celsius temperature of Object X greater than 50" is No. However, if C = 100, the answer to the question "Is the Celsius temperature of Object X greater than 50" is Yes.
As we are obtaining two contradicting answers to the question, we can eliminate A and D.
Statement 2
(2) F - C > 72
F = \(\frac{9}{5}\)C + 32
Multiplying by 5 on both sides of the equation we get
5F = 9C + 160 --- (1)
Statement 2 -
F - C > 72
Multiplying by 5 on both sides of the inequality we get
5F - 5C > 360
From (1)
9C + 160 - 5C > 360
4C > 200
C > 50
Hence, the Celsius temperature of Object X is greater than 50.
This statement is sufficient to answer the question, "Is the Celsius temperature of Object X greater than 50 ? ".
Option B
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
General Discussion
Subliminal
Joined: 13 Nov 2018
Last visit: 12 Sep 2026
Posts: 12
Location: India
GRE 1: Q800 V530
GRE 2: Q170 V160
WE:Education (Education)
Here's my solution for this question:
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29th Jan _ Post 2_QD.jpeg [ 146.26 KiB | Viewed 10113 times ]
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29th Jan _ Post 2_St1.jpeg [ 67.13 KiB | Viewed 9793 times ]
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gmatophobia
Slight calculation mistake for the first option- the reciprocal would be C > \(\frac{88*5}{9}\)
and that would explain the <50C
Learn to substitute F
750-scorer — ~45 sec
Given:
F = (9/5)C + 32
Question: Is C > 50?
Key approach: Translate each statement directly into a condition on C.
1. F > 120
(9/5)C + 32 > 120
(9/5)C > 88
C > 48.89
This allows C = 49 and C = 51.
Insufficient.
2. F - C > 72
Substitute:
(9/5)C + 32 - C > 72
(4/5)C > 40
C > 50
This exactly answers the question.
Sufficient.
Answer: B
Transferable learning:
For DS questions with a given equation, immediately substitute the equation into each statement and check whether it gives the exact threshold being asked.
Do not solve for both variables unnecessarily.
Here:
Statement 1 → C > 48.89 → does not establish whether C > 50
Statement 2 → C > 50 → exactly answers the question
750-scorer — ~45 sec
Given:
F = (9/5)C + 32
Question: Is C > 50?
Key approach: Translate each statement directly into a condition on C.
1. F > 120
(9/5)C + 32 > 120
(9/5)C > 88
C > 48.89
This allows C = 49 and C = 51.
Insufficient.
2. F - C > 72
Substitute:
(9/5)C + 32 - C > 72
(4/5)C > 40
C > 50
This exactly answers the question.
Sufficient.
Answer: B
Transferable learning:
For DS questions with a given equation, immediately substitute the equation into each statement and check whether it gives the exact threshold being asked.
Do not solve for both variables unnecessarily.
Here:
Statement 1 → C > 48.89 → does not establish whether C > 50
Statement 2 → C > 50 → exactly answers the question
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