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16 Jun 2025, 08:43
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
100% (00:24) correct
0% (00:00) wrong based on 5 sessions
History
Date
Time
Result
Not Attempted Yet
For any positive integer a, let !a! denote the smallest prime factor of a. Which of the following is equal to !35!?
A. !10!
B. !15!
C. !45!
D. !55!
E. !75!
A. !10!
B. !15!
C. !45!
D. !55!
E. !75!
17 Jun 2025, 21:36
Kudos
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Given: For any positive integer a, we define !a! = the smallest prime factor of a.
To find: The choice that has the same value as !35!.
Solution:
Step 1: Compute !35!
Step 2: Find the choice that also equals 5
A. !10!
B. !15!
C. !45!
D. !55!
We do not need to check further.
Correct Answer: D
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
To find: The choice that has the same value as !35!.
Solution:
Step 1: Compute !35!
- Prime Factors of 35 are: 5 and 7.
- Clearly, the smallest prime factor = 5.
- Thus, !35! = 5.
Step 2: Find the choice that also equals 5
A. !10!
- Prime factors of 10: 2, 5
- Smallest = 2 ≠ 5
B. !15!
- Prime factors of 15: 3, 5
- Smallest = 3 ≠ 5
C. !45!
- Prime factors of 45: 3, 5
- Smallest = 3 ≠ 5
D. !55!
- Prime factors of 55: 5, 11
- Smallest = 5
We do not need to check further.
Correct Answer: D
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
19 Jun 2025, 12:52
Kudos
Bookmarks
OE
Check the first few primes; 35 is not divisible by 2 or 3, but is divisible by 5, so 5 is the smallest prime factor of 35: !35! = 5. Now check the five choices: !10! = 2, and !15! , !45! , and !75! are all equal to 3. Only !55! = 5.
The answer is D.
The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of each of them. For example, the LCM of 6 and 10 is 30. Infinitely many positive integers are multiples of both 6 and 10, including 60, 90, 180, 600, 6000, and 66,000,000, but 30 is the smallest one.
The greatest common factor (GCF) or greatest common divisor (GCD) of two or more integers is the largest integer that is a factor of each of them. For example, the only positive integers that are factors of both 6 and 10 are 1 and 2, so the GCF of 6 and 10 is 2. For small numbers, you can often find their GCF and LCM by inspection.
Check the first few primes; 35 is not divisible by 2 or 3, but is divisible by 5, so 5 is the smallest prime factor of 35: !35! = 5. Now check the five choices: !10! = 2, and !15! , !45! , and !75! are all equal to 3. Only !55! = 5.
The answer is D.
The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of each of them. For example, the LCM of 6 and 10 is 30. Infinitely many positive integers are multiples of both 6 and 10, including 60, 90, 180, 600, 6000, and 66,000,000, but 30 is the smallest one.
The greatest common factor (GCF) or greatest common divisor (GCD) of two or more integers is the largest integer that is a factor of each of them. For example, the only positive integers that are factors of both 6 and 10 are 1 and 2, so the GCF of 6 and 10 is 2. For small numbers, you can often find their GCF and LCM by inspection.
