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If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?
1) N is divisible by 3 ?
2) N is divisible by 7 ?
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'A'. Can you explain this answer?
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If K is a positive integer less than 10 and N = 4,321 + K, what is the...
Ans.
Method to Solve :
N = 4321 + K (where K is a positive integer less than 10)
So the possible values of N are 4322 to 4330 inclusive.
1. N is divisible by 3.
The sum of the digits must be a multiple of 3.
4+3+2 = 9. So the 4th digit must be 3,6 or 9. 4330 is not a multiple of 3.
So possible values for N are : 4323, 4326, and 4329. So K = 2, 5 or 8.
INSUFFICIENT.
2. N is divisible by 7.
First find out the remainder for the lowest value of N i.e. 4322 . This is = 617 remainder 3
So the next value of N which is divisible by 7 is 4322 + 4 = 4326 which is 618*7
After this the next multiple is 619*7 = 4333 which is outside the range for N
Thus the value of N must be 4326. So K = 5
So the possible values of N are 4322 to 4330 inclusive.
1. N is divisible by 3.
The sum of the digits must be a multiple of 3.
4+3+2 = 9. So the 4th digit must be 3,6 or 9. 4330 is not a multiple of 3.
So possible values for N are : 4323, 4326, and 4329. So K = 2, 5 or 8.
INSUFFICIENT.
2. N is divisible by 7.
First find out the remainder for the lowest value of N i.e. 4322 . This is = 617 remainder 3
So the next value of N which is divisible by 7 is 4322 + 4 = 4326 which is 618*7
After this the next multiple is 619*7 = 4333 which is outside the range for N
Thus the value of N must be 4326. So K = 5
Most Upvoted Answer
If K is a positive integer less than 10 and N = 4,321 + K, what is the...
Given: K is a positive integer less than 10 and N = 4,321 + K
If K is a positive integer less than 10, then K = 1, 2, 3, 4, ... or 9
So, 4321 + K (aka N) can have 9 possible values.
In other word, N = 4322, 4323, 4324, ..., 4330 (9 consecutive integers)
Statement 1: N is divisible by 3
IMPORTANT RULE: Among a set of consecutive integers, every 3rd integer will be divisible by 3.
Likewise, every 4th integer will be divisible by 4.
Every 5th integer will be divisible by 5.
Etc.
So, in a set of consecutive integers, about 1/3 of them will be divisible by 3.
Since N can be any of the 9 consecutive integers from 4322 to 4330, and since 1/3 of these 9 integers are divisible by 3, we can conclude that N could have 3 possible values.
Aside: We need not determine what these 3 possible values are, but if we were to find them, we'd see that N could equal 4323, 4326 or 4329
Since we cannot answer the target question with certainty, statement 1 is not sufficient.
Statement 2: N is divisible by 7
Using our rule from earlier, about 1/7 of the 9 integers are divisible by 7, so in this case, it's possible that there's 1 value for N or possibly 2 values.
So, we need to check.
We'll look for a multiple of 7 among the possible values of N (4322, 4323, 4324, ..., 4330)
We know that 4200 is divisible by 7
So, 4270 is divisible by 7 (added 70 to 4200)
Which means 4340 is divisible by 7 (added 70 to 4270)
Oh, we've gone to far.
4333 is divisible by 7 (subtracted 7 from 4340)
4326 is divisible by 7 (subtracted 7 from 4333)
Since every 7th integer is divisible by 7, we can see that N could equal ... 4212, 4219, 4326, 4333, 4340,...
Since only one of these values is in the range of possible values of N (4322, 4323, 4324, ..., 4330), we can be certain that N = 4326
If K is a positive integer less than 10, then K = 1, 2, 3, 4, ... or 9
So, 4321 + K (aka N) can have 9 possible values.
In other word, N = 4322, 4323, 4324, ..., 4330 (9 consecutive integers)
Statement 1: N is divisible by 3
IMPORTANT RULE: Among a set of consecutive integers, every 3rd integer will be divisible by 3.
Likewise, every 4th integer will be divisible by 4.
Every 5th integer will be divisible by 5.
Etc.
So, in a set of consecutive integers, about 1/3 of them will be divisible by 3.
Since N can be any of the 9 consecutive integers from 4322 to 4330, and since 1/3 of these 9 integers are divisible by 3, we can conclude that N could have 3 possible values.
Aside: We need not determine what these 3 possible values are, but if we were to find them, we'd see that N could equal 4323, 4326 or 4329
Since we cannot answer the target question with certainty, statement 1 is not sufficient.
Statement 2: N is divisible by 7
Using our rule from earlier, about 1/7 of the 9 integers are divisible by 7, so in this case, it's possible that there's 1 value for N or possibly 2 values.
So, we need to check.
We'll look for a multiple of 7 among the possible values of N (4322, 4323, 4324, ..., 4330)
We know that 4200 is divisible by 7
So, 4270 is divisible by 7 (added 70 to 4200)
Which means 4340 is divisible by 7 (added 70 to 4270)
Oh, we've gone to far.
4333 is divisible by 7 (subtracted 7 from 4340)
4326 is divisible by 7 (subtracted 7 from 4333)
Since every 7th integer is divisible by 7, we can see that N could equal ... 4212, 4219, 4326, 4333, 4340,...
Since only one of these values is in the range of possible values of N (4322, 4323, 4324, ..., 4330), we can be certain that N = 4326
Since we can answer the target question with certainty, statement 2 is Sufficient.
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If K is a positive integer less than 10 and N = 4,321 + K, what is the...
To find the value of K, we need to determine if N = 4,321 is divisible by K. Let's analyze each statement:
Statement 1: N is divisible by 3
- If N is divisible by 3, it means that the sum of its digits is divisible by 3.
- The sum of the digits of N = 4,321 is 4 + 3 + 2 + 1 = 10, which is not divisible by 3.
- Therefore, N is not divisible by 3, which means K cannot be 3.
- However, there are still other possible values of K that could satisfy the condition, as K could be any positive integer less than 10 excluding 3.
- This statement alone is not sufficient to determine the value of K.
Statement 2: N is divisible by 7
- If N is divisible by 7, it means that when N is divided by 7, the remainder is 0.
- N = 4,321 when divided by 7 gives a remainder of 4.
- Therefore, N is not divisible by 7, which means K cannot be 7.
- However, there are still other possible values of K that could satisfy the condition, as K could be any positive integer less than 10 excluding 7.
- This statement alone is not sufficient to determine the value of K.
Combining both statements:
- From statement 1, we know that K cannot be 3.
- From statement 2, we know that K cannot be 7.
- Therefore, the only possible value of K that satisfies both statements is K = 1.
- Both statements together are sufficient to determine the value of K.
Hence, the correct answer is option A: Exactly one of the statements can answer the question.
Statement 1: N is divisible by 3
- If N is divisible by 3, it means that the sum of its digits is divisible by 3.
- The sum of the digits of N = 4,321 is 4 + 3 + 2 + 1 = 10, which is not divisible by 3.
- Therefore, N is not divisible by 3, which means K cannot be 3.
- However, there are still other possible values of K that could satisfy the condition, as K could be any positive integer less than 10 excluding 3.
- This statement alone is not sufficient to determine the value of K.
Statement 2: N is divisible by 7
- If N is divisible by 7, it means that when N is divided by 7, the remainder is 0.
- N = 4,321 when divided by 7 gives a remainder of 4.
- Therefore, N is not divisible by 7, which means K cannot be 7.
- However, there are still other possible values of K that could satisfy the condition, as K could be any positive integer less than 10 excluding 7.
- This statement alone is not sufficient to determine the value of K.
Combining both statements:
- From statement 1, we know that K cannot be 3.
- From statement 2, we know that K cannot be 7.
- Therefore, the only possible value of K that satisfies both statements is K = 1.
- Both statements together are sufficient to determine the value of K.
Hence, the correct answer is option A: Exactly one of the statements can answer the question.
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If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?1) N is divisible by 3 ?2) N is divisible by 7 ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?
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