Q1
a and b are integers such that a/b =3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?
a) 3 b)9 c)36 d)81 E)144
I understand how to derive the equation to 20 X R = 9 X b.
Lost on how the correct answer is a) (3).
Q2
When 15 is divided by y, the remainder is y - 3. If Y must be an integer, what are all the
possible values of y?
Understand the remainder,y, must be at least 3 and y at most can only be 18.
From this point you could pick numbers, dividing 15 by these numbers to check to see whether the
remainder is 3 lower than the number you have picked. Only 15 divided by 3,6,9, and 18 yield remainders
three less than the divisor:
15 = (5 x3) + 0
15 = (2 x 6) + 3
15 = (1 x 9) + 6
15 = (0 x 18) + 15
Remainder of 0 is 3 less than divisor of 3.
Remainder of 3 is 3 less than divisor of 6.
Remainder of 6 is 3 less than divisor of 9.
Remainder of 15 is 3 less than divisor of 18.
answer is 3,6,9,18. Still dont understand.
Please explain.
Thanks and regards
Charles
Number Properties - Advanced
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Say, when a is divided by b, the quotient is x.davo45 wrote:a and b are integers such that a/b =3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?
a) 3 b)9 c)36 d)81 E)144
Hence, a = bx + R
But, a/b = 3.45 => a = 3.45b = 3b + .45b
As a, b and R are integers, comparing the terms, x must be equal to 3 and R must be equal to 0.45b.
Hence, for b to be integer, (R/0.45) must be an integer.
For R = 3, (R/.45) is not an integer, i.e. 3 cannot be a value of R.
The correct answer is A.
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a/b=345/100 --> 69/20
69/20 = 3 +9/20
69*4/20*4 = 3 + 36/80
69*9/20*9 = 3 + 81/180
69*16/20*16 = 3 + 144/320
Only 3 cannot be remainder
correct answer is A.
69/20 = 3 +9/20
69*4/20*4 = 3 + 36/80
69*9/20*9 = 3 + 81/180
69*16/20*16 = 3 + 144/320
Only 3 cannot be remainder
correct answer is A.
davo45 wrote:Q1
a and b are integers such that a/b =3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?
a) 3 b)9 c)36 d)81 E)144
Thanks and regards
Charles
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15/y = i (i is integer) + (y-3)/y --> 15/y = i + 1 -3/y --> 15/y +3/y = i + 1 --> 18/y = i + 1;
y= 18/(i+1), y can be an integer if and only if 18 divided by (i+1) gives an integer; this is possible when i has the following values {0,1,2,5,8,17}. Total six values for i and six values for y {18,9,6,3,2,1}
y= 18/(i+1), y can be an integer if and only if 18 divided by (i+1) gives an integer; this is possible when i has the following values {0,1,2,5,8,17}. Total six values for i and six values for y {18,9,6,3,2,1}
davo45 wrote:
Q2
When 15 is divided by y, the remainder is y - 3. If Y must be an integer, what are all the
possible values of y?
Understand the remainder,y, must be at least 3 and y at most can only be 18.
From this point you could pick numbers, dividing 15 by these numbers to check to see whether the
remainder is 3 lower than the number you have picked. Only 15 divided by 3,6,9, and 18 yield remainders
three less than the divisor:
15 = (5 x3) + 0
15 = (2 x 6) + 3
15 = (1 x 9) + 6
15 = (0 x 18) + 15
Remainder of 0 is 3 less than divisor of 3.
Remainder of 3 is 3 less than divisor of 6.
Remainder of 6 is 3 less than divisor of 9.
Remainder of 15 is 3 less than divisor of 18.
answer is 3,6,9,18. Still dont understand.
Please explain.
Thanks and regards
Charles
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1)
.45 = X/b (as per formula)
45/100 = X/b
9/20 =X/b (reduce)
now 9,36,81,144 are all multiples of 9 so they cannot be the answer.
3 is not a multiple of 9 and is our choice.
.45 = X/b (as per formula)
45/100 = X/b
9/20 =X/b (reduce)
now 9,36,81,144 are all multiples of 9 so they cannot be the answer.
3 is not a multiple of 9 and is our choice.
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When one positive integer doesn't divide evenly into another positive integer, we can represent what's left over as a decimal (5/2 = 2.5) or as a remainder (5/2 = 2 R 1). The problem above is testing the relationship between the decimal representation and the remainder representation. Here's the relationship:Q1
a and b are integers such that a/b =3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?
a) 3 b)9 c)36 d)81 E)144
I understand how to derive the equation to 20 X R = 9 X b.
decimal * divisor = remainder
Let's revisit 5/2 = 2.5. If we multiply the decimal (.5) by the divisor (2), we get .5 * 2 = 1, which is the remainder if we represent the division as 5/2 = 2 R1.
In the problem above. the decimal is .45, the divisor is b, and the answer choices represent possible remainders. The correct answer -- the answer that cannot be the value of R -- will yield a non-integer value for b.
Answer choice A: R = 3
.45b = 3
b = 3/.45 = 300/45 = 20/3.
The correct answer is A.
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Step-by-step method for dealing with remainder questions when picking numbers or plugging in answers doesn't apply:
1) Rephrase as equation: remainder = decimal x divisor
R = .45b
2) Rephrase decimal using 10^-x
R = 45 x 10^-2b
3) Prime factor all terms
R = 3^2 x 5 x 2^-2 x 5^-2 x b
4) Combine terms
R = 2^-2 x 3^2 x 5^-2 x b
5) Rephrase as ratio/fraction:
R/b = 3^2/5 x 2^2
We now know that R must be a multiple of 9 (and that b must be multiple of 20).[/u]
15/y = i (i is integer) + (y-3)/y --> 15/y = i + 1 -3/y --> 15/y +3/y = i + 1 --> 18/y = i + 1;
y= 18/(i+1), y can be an integer if and only if 18 divided by (i+1) gives an integer; this is possible when i has the following values {0,1,2,5,8,17}. Total six values for i and six values for y {18,9,6,3,2,1}
can you please clarify me how did you come to (y-3)/y ? everything else from there is clear but in the question it says:: When 15 is divided by y, the remainder is y - 3. I just can not understand how did you come to (y-3)/y
y= 18/(i+1), y can be an integer if and only if 18 divided by (i+1) gives an integer; this is possible when i has the following values {0,1,2,5,8,17}. Total six values for i and six values for y {18,9,6,3,2,1}
can you please clarify me how did you come to (y-3)/y ? everything else from there is clear but in the question it says:: When 15 is divided by y, the remainder is y - 3. I just can not understand how did you come to (y-3)/y
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@aljaz11, hi the selection (made by me) was your question, correct? Let me ask you - when 15 is divided by 2, the remainder is 1, how you understand the remainder 1/15? The same way I consider "When 15 is divided by y and the remainder is y-3 --> 15/y= integer + (y-3)/y. anything else, please post that
aljaz11 wrote:15/y = i (i is integer) + (y-3)/y --> 15/y = i + 1 -3/y --> 15/y +3/y = i + 1 --> 18/y = i + 1;
y= 18/(i+1), y can be an integer if and only if 18 divided by (i+1) gives an integer; this is possible when i has the following values {0,1,2,5,8,17}. Total six values for i and six values for y {18,9,6,3,2,1}
can you please clarify me how did you come to (y-3)/y ? everything else from there is clear but in the question it says:: When 15 is divided by y, the remainder is y - 3. I just can not understand how did you come to (y-3)/y
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hi, yes that was what i was asking you about
i must admit i still dont comprehend the (y-3)/y im trying hard
you gave an example:
15 is divided by 2 the remainder is 1 or 1/15.... i do understand that remainder of 1 is 1/15 of 15 (or 1part out of 15) but if we divide 15 by 2 we get 7 and the remainder is a whole number 1 (or 15/15...thats where i am confused with 1/15)
im just having trouble trying to cross this gap.... thanks for the help!!
i must admit i still dont comprehend the (y-3)/y im trying hard
you gave an example:
15 is divided by 2 the remainder is 1 or 1/15.... i do understand that remainder of 1 is 1/15 of 15 (or 1part out of 15) but if we divide 15 by 2 we get 7 and the remainder is a whole number 1 (or 15/15...thats where i am confused with 1/15)
im just having trouble trying to cross this gap.... thanks for the help!!
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the fact that we have remainder puts zero possibility on having 0 as a remainder - otherwise there's no remainder; i is just an integer to give us a remainder with having 15 divided by y as well as remainder has the form (y-3)/y, ok?
aljaz11 wrote:hi, yes that was what i was asking you about
i must admit i still dont comprehend the (y-3)/y im trying hard
you gave an example:
15 is divided by 2 the remainder is 1 or 1/15.... i do understand that remainder of 1 is 1/15 of 15 (or 1part out of 15) but if we divide 15 by 2 we get 7 and the remainder is a whole number 1 (or 15/15...thats where i am confused with 1/15)
im just having trouble trying to cross this gap.... thanks for the help!!
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com