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A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A bag contains only two types of coins: 10 cent coins or 1 dollar coin...
Steps 1 & 2: Understand Question and Draw Inferences
If the number of 10-cent coins are ‘x’ and the number of 1-dollar coins is ‘y’, then we are told that x is less than or equal to y. The question is: what is the value of x?
Also, note that since ‘x’ and ‘y’ are number of coins, they must be non-negative integers.
Step 3: Analyze Statement 1
The total money in the bag due to 10-cent coins = 10x cents
The total money in the bag due to 1-dollar coins = y dollars or 100y cents
Total money in the bag = Total money due to 10-cent coins + Total money due to 1-dollar coins
16.50 * 100 = 10x + 100y
1650 = 10x + 100y
165 = x + 10y
This equation can have several integral solutions such as
if x = 5, y = 16
if x = 15, y = 15
if x = 25, y = 14, and so on.
Since x is less than equal to y, only the first two solutions are possible. ‘x’, whose value has to be found, can be 5 or 15.
INSUFFICIENT.
Step 4: Analyze Statement 2
If five 10-cent coins are replaced with five 1-dollar coins then the number of 10-cent coins become x – 5 and the number of 1-dollar coins become y + 5.
Then, y+5 = 2/3 * (x+y)
3y + 15 = 2x + 2y
y = 2x -15 ------(1)
We have to remember that x and y can only take non-negative integral values and x≤y
Substituting y from equation (1) in the given inequality, we have
x≤2x−15x≥15
x can have any value greater than or equal to 15.
For example,
if x = 15, then y = 2(15) – 15 = 15
if x = 16, then y = 2(16) – 15 = 17
and so on.
INSUFFCIENT.
Step 5: Analyze both statements together (if needed)
According to the information provided in Statement 1, x = 5 or x = 15.
According to the information provided in Statement 2, x = 15 or x = 16 or x = 17 and so on.
The common solution from the two statements is that x = 15
SUFFICIENT.
(C) is the correct answer.
Most Upvoted Answer
A bag contains only two types of coins: 10 cent coins or 1 dollar coin...
Statement (1): The total amount of money in the bag is $16.50.
This statement gives us information about the total value of the coins in the bag, but it doesn't provide any information about the specific number of 10 cent coins or 1 dollar coins. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2): If five 10-cent coins are removed and replaced with five 1-dollar coins, then two-thirds of all the coins in the bag are 1 dollar coins.
Let's analyze this statement. Suppose the bag initially contains x 10 cent coins and y 1 dollar coins. After replacing five 10 cent coins with five 1 dollar coins, the total number of coins in the bag remains the same, but the ratio of 10 cent coins to 1 dollar coins changes.
Before replacement:
Number of 10 cent coins = x
Number of 1 dollar coins = y
Total number of coins = x + y
After replacement:
Number of 10 cent coins = x - 5
Number of 1 dollar coins = y + 5
Total number of coins = (x - 5) + (y + 5) = x + y
According to the statement, two-thirds of the coins in the bag are 1 dollar coins after the replacement. This can be expressed as:
(y + 5)/(x + y) = 2/3
Simplifying this equation, we get:
3(y + 5) = 2(x + y)
3y + 15 = 2x + 2y
15 - 3y = 2x - y
15 = x + y
From this equation, we can see that the total number of coins in the bag is 15.
Now, let's consider the possible values for x and y that satisfy this equation while also satisfying the condition that the number of 10 cent coins does not exceed the number of 1 dollar coins.
Since the total number of coins is 15, we can have the following combinations:
- x = 0, y = 15
- x = 1, y = 14
- x = 2, y = 13
- x = 3, y = 12
- x = 4, y = 11
- x = 5, y = 10
Out of these combinations, only x = 5 and y = 10 satisfy the condition that the number of 10 cent coins does not exceed the number of 1 dollar coins.
Therefore, statement (2) alone is sufficient to answer the question.
Conclusion:
From our analysis, we can see that statement (2) alone is sufficient to answer the question, while statement (1) alone is not sufficient. Therefore, the correct answer is option (b) "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient."
This statement gives us information about the total value of the coins in the bag, but it doesn't provide any information about the specific number of 10 cent coins or 1 dollar coins. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2): If five 10-cent coins are removed and replaced with five 1-dollar coins, then two-thirds of all the coins in the bag are 1 dollar coins.
Let's analyze this statement. Suppose the bag initially contains x 10 cent coins and y 1 dollar coins. After replacing five 10 cent coins with five 1 dollar coins, the total number of coins in the bag remains the same, but the ratio of 10 cent coins to 1 dollar coins changes.
Before replacement:
Number of 10 cent coins = x
Number of 1 dollar coins = y
Total number of coins = x + y
After replacement:
Number of 10 cent coins = x - 5
Number of 1 dollar coins = y + 5
Total number of coins = (x - 5) + (y + 5) = x + y
According to the statement, two-thirds of the coins in the bag are 1 dollar coins after the replacement. This can be expressed as:
(y + 5)/(x + y) = 2/3
Simplifying this equation, we get:
3(y + 5) = 2(x + y)
3y + 15 = 2x + 2y
15 - 3y = 2x - y
15 = x + y
From this equation, we can see that the total number of coins in the bag is 15.
Now, let's consider the possible values for x and y that satisfy this equation while also satisfying the condition that the number of 10 cent coins does not exceed the number of 1 dollar coins.
Since the total number of coins is 15, we can have the following combinations:
- x = 0, y = 15
- x = 1, y = 14
- x = 2, y = 13
- x = 3, y = 12
- x = 4, y = 11
- x = 5, y = 10
Out of these combinations, only x = 5 and y = 10 satisfy the condition that the number of 10 cent coins does not exceed the number of 1 dollar coins.
Therefore, statement (2) alone is sufficient to answer the question.
Conclusion:
From our analysis, we can see that statement (2) alone is sufficient to answer the question, while statement (1) alone is not sufficient. Therefore, the correct answer is option (b) "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient."
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A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?
Question Description
A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
Solutions for A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Here you can find the meaning of A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?(1) The total amount of money in the bag is $16.50.(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
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