A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?
A) 9
B) 14
C) 20
D) 6
E) 15
The OA is E.
How can I do this PS question? Can I find what is the number? I could not do it. Help.
A number when divided by 105 leaves 99 as remainder.
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When x is divided by y, the remainder is R.Vincen wrote:A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?
A) 9
B) 14
C) 20
D) 6
E) 15
Given this information, the smallest possible value for x is R.
A number when divided by 105 leaves 99 as remainder.
According to the rule in blue, the smallest possible option for the number is 99.
When 99 is divided by 21, we get:
99/21 = 4 R15.
The correct answer is E.
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A lot of integer properties questions can be solved by plugging in numbers.Vincen wrote:A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?
A) 9
B) 14
C) 20
D) 6
E) 15
In this case, we'll use a nice nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Now onto the question......
A number when divided by 105 leaves 99 as remainder
Possible values of the number: 99, 99+105, 99+(2)(105), 99+(3)(105), 99+(4)(105), etc
We can use ANY of the above values to answer the question.
So, let's use the smallest value (99)
What will be the remainder if the number is divided by 21?
99 divided by 21 equals 4 with remainder 15
Answer: E
Notice that we get the same result if we test other possible values.
For example, let's test the next possible value: 99+105
99+105 = 204
204 divided by 21 equals 9 with remainder 15
Answer: still E
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We could cheat and say that
a number = 105 + 99
a number = 204
From here, find the remainder when 204 is divided by 21, and you're done!
a number = 105 + 99
a number = 204
From here, find the remainder when 204 is divided by 21, and you're done!
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Let me also add a more conceptual approach.
Let's say that our number = 105*something + 99.
When I divide that number by 21, I get
(105*something + 99)/21 =>
105*something/21 + 99/21 =>
5*something + 99/21
Now we can see the remainder will come entirely from the second part, 99/21. 99 = 4*21 + 15, so our remainder is that last part, the +15.
Let's say that our number = 105*something + 99.
When I divide that number by 21, I get
(105*something + 99)/21 =>
105*something/21 + 99/21 =>
5*something + 99/21
Now we can see the remainder will come entirely from the second part, 99/21. 99 = 4*21 + 15, so our remainder is that last part, the +15.
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- Scott@TargetTestPrep
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We can let n = the number and we have:Vincen wrote:A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?
A) 9
B) 14
C) 20
D) 6
E) 15
n = 105Q + 99
Thus, when that number is divided by 21, we have:
(105Q + 99)/21
5Q + 99/21
Since 5Q is an integer, the remainder will come from 99 divided by 21:
99/21 = 4 R 15
We see that the remainder is 15.
Answer: E
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