If T is a prime number, what is the remainder when T is divided by 3?(1) (T 13)3 is divisible by 48(2) 4T 3 leaves a remainder 1 when divided by 18a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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If T is a prime number, what is the remainder when T is divided by 3?

(1) (T – 13)³ is divisible by 48

(2) 4T – 3 leaves a remainder 1 when divided by 18

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'D'. Can you explain this answer?

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Test: Divisibility And Remainders- 1

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If T is a prime number, what is the remainder when T is divided by 3?(...

Steps 1 & 2: Understand Question and Draw Inferences

Given: Prime Number T

To find: Remainder when T is divided by 3

To answer this, we need to express T in the form 3k + r where k is an integer and r = {0, 1, 2}
Please note that r = 0, only in the case when T = 3. For all the other values of T, T will not be divisible by 3.

Step 3: Analyze Statement 1 independently

(T – 13)³ is divisible by 48
- 48 = 2⁴ * 3
Since T is an integer, T – 13 will be an integer as well. Let T – 13 = N
So we can write: N³ is divisible by 2⁴ and by 3
- Since N³ is divisible by 2⁴, N must be divisible by 2²

Explanatory note:
1. Since N³ is divisible by an even number (2⁴), this means that 2 is definitely a prime factor of N³, and hence, of N
2. So, we can write: N = 2^a * P₂^b *P₃^c * . . . , where P₂, P₃ etc. are the other prime factors of N
3. And, N³ = 2^3a * P₂^3b *P₃^3c * . . . ,
4. Since N³ is divisible by 2⁴, this means: 2^3a≥2⁴
5. Comparing the powers of 2, we can write: 3a≥4
6. That is, a≥4/3
7. Since N is an integer, the power of 2 cannot be a fraction. So, a must be an integer as well
8. What is the smallest integer that is greater than 4/3 ? It is 2
9. So, a_min = 2
10. Thus, N must be divisible by 2²

Thus, N is divisible by 2² (that is, 4) and by 3
- Least common multiple of 4 and 3 is 12
- Thus, N is divisible by 12

So T – 13 is divisible by 12
- T – 13 is of the form 12q, where q is some integer
- T = 12q + 13
- T = 12q + 12 + 1
- T = 12(q + 1) + 1
- In the above expression, the term 12(q+1) is divisible by 3. Let the quotient when this term is divided by 3 be k
- So, we can write: T = 3k + 1

Therefore, Remainder r = 1

Statement 1 alone is sufficient to answer the question.

Step 4: Analyze Statement 2 independently

4T – 3 leaves a remainder 1 when divided by 18
- So, we can write: 4T – 3 = 18m + 1, where quotient m is some integer
- 4T - 4 = 18m
2T - 2 = 9m
Since m is an integer, the product 2(T - 1) must be divisible by 9
- In this product, 2 is clearly not divisible by 9
- So, T – 1 must be divisible by 9
So, we can write: T – 1 =9z, where z is some integer
Thus T = 9z + 1
In the above expression, the term 9z is divisible by 3
So, the remainder obtained when T is divided by 3 is 1
Thus, Statement 2 alone is also sufficient to obtain a unique answer

Step 5: Analyze Both Statements Together (if needed)

Since we’ve arrived at a unique answer in each of Steps 3 and 4, this step is not required

Answer: Option D

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If T is a prime number, what is the remainder when T is divided by 3?(1) (T – 13)3 is divisible by 48(2) 4T – 3 leaves a remainder 1 when divided by 18a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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If T is a prime number, what is the remainder when T is divided by 3?(1) (T – 13)3 is divisible by 48(2) 4T – 3 leaves a remainder 1 when divided by 18a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If T is a prime number, what is the remainder when T is divided by 3?(1) (T – 13)3 is divisible by 48(2) 4T – 3 leaves a remainder 1 when divided by 18a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If T is a prime number, what is the remainder when T is divided by 3?(1) (T – 13)3 is divisible by 48(2) 4T – 3 leaves a remainder 1 when divided by 18a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.

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