X = a.bcIf a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc? (1) 100X divided by 50 leaves a remainder 24 (2) 1000X divided by 8 leaves a remainder 0a)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 'E'. Can you explain this answer?

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X = a.bc

If a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc?

(1) 100X divided by 50 leaves a remainder 24

(2) 1000X divided by 8 leaves a remainder 0

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 'E'. Can you explain this answer?

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Test: Divisibility And Remainders- 1

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X = a.bcIf a, b and c denote the units, tenths and hundredths digits i...

Steps 1 & 2: Understand Question and Draw Inferences

Step 3: Analyze Statement 1 independently

100X divided by 50 leaves a remainder 24
So, we can write: 100X=50k+24

, where k is an integer . . . (I)
From the given expression of X, we can write:
100X=100a+10b+c . . . (II)

The units digit on left hand side of the equation = c
The units digit on right hand side of the equation = 4
This means, c = 4

As a multiple of 5 always has its units digit equal to either 0 or 5, 5k + 2 will always have its units digit equal to 2 or 7. So, b = {2, 7}.
However, a can have many more values.
Thus, we only know the definite value of c
- But we do not know definite values of a and b
Thus, we know a definite value of c
- But we do not know definite values of a and b
So, we will not be able to find a definite value of the product a×b×c

Statement 1 is not sufficient to answer the question.

Step 4: Analyze Statement 2 independently

- 1000a is always divisible by 8 as 1000 is divisible by 8
- 100b will be divisible by 8, only if b is even
  - b= {0, 2, 4, 6, 8}
- 10c will be divisible by 8 only if c = {4, 8}
As we do not have unique values of a, b and c we cannot calculate the unique value of product of a, b and c

Therefore, Statement 2 is clearly not sufficient

Step 5: Analyze Both Statements Together (if needed)

From Statement 1: c = 4 and 10a+b=5k+2

, where k is an integer

From Statement 2: b = {0, 2, 4, 6, 8} and c = {4, 8}

So even after combining both statements, we still don’t know the definite values of a and b, and therefore cannot find a unique value of the product a×b×c

The two statements together are not sufficient to answer the question.

Answer: Option E

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Most Upvoted Answer

X = a.bcIf a, b and c denote the units, tenths and hundredths digits i...

Understanding the Problem
We are tasked with finding the product abc, where X = a.bc represents a decimal number with a as the unit digit, b as the tenths digit, and c as the hundredths digit.
Analyzing the Statements
Statement (1): 100X divided by 50 leaves a remainder 24.
- This can be expressed as:
100X = 50k + 24 for some integer k.
- Rearranging gives:
X = (50k + 24) / 100.
- This indicates that X can take various values depending on k, which will impact the digits a, b, and c.
- Since we lack specific values for a, b, and c, we cannot determine abc uniquely.
Statement (2): 1000X divided by 8 leaves a remainder 0.
- This implies:
1000X = 8m for some integer m.
- Thus, X = (8m) / 1000.
- Similar to Statement (1), this gives us a range of possible values for X.
- Without specific values for a, b, and c, we cannot uniquely determine the product abc.
Conclusion
- Independently Insufficient: Each statement alone does not provide enough information to determine the specific values of a, b, and c.
- Combined Insufficient: Even when combined, the statements do not yield a specific value for abc, as they still leave the digits undetermined.
Thus, the correct answer is option E: Statements (1) and (2) together are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Answered by Talent Skill Learning · View profile

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X = a.bcIf a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc? (1) 100X divided by 50 leaves a remainder 24 (2) 1000X divided by 8 leaves a remainder 0a)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 'E'. Can you explain this answer?

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X = a.bcIf a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc? (1) 100X divided by 50 leaves a remainder 24 (2) 1000X divided by 8 leaves a remainder 0a)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 'E'. 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 X = a.bcIf a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc? (1) 100X divided by 50 leaves a remainder 24 (2) 1000X divided by 8 leaves a remainder 0a)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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X = a.bcIf a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc? (1) 100X divided by 50 leaves a remainder 24 (2) 1000X divided by 8 leaves a remainder 0a)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 'E'. Can you explain this answer?.

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