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If i and d are integers, what is the value of i? (1) The remainder wh

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Bunuel
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If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] New post   12 May 2021, 05:30
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If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(2) The quotient when i is divided by (d+2) is d
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Bunuel
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Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] New post   15 May 2021, 02:45
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Bunuel wrote:
If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(2) The quotient when i is divided by (d+2) is d


It can be done algebraically but picking numbers would probably be faster/easier.

If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d --> let the remainder be 0 to simplify the case. So, we have that i is divisible by both d and d+2 --> if d=1 then d+2=3 and i can be ANY multiple of 3. Not sufficient.

(2) The quotient when i is divided by (d+2) is d --> let the remainder be 0 to simplify the case. Now, if d=2 then d+2=4, so i=8 (8/4=2: i=8 divided by d+2=4 yields the quotient of d=2) but if d=3 then d+2=5 and i=15 (15/5=3). Not sufficient.

(1)+(2) Notice that two values of i from (2) works for (1) as well: 8 is divisible d=2 and d+2=4 and 15 is divisible by d=3 and d+2=5.

Answer: E.

Hope it's clear.
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Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] New post   12 May 2021, 07:02
No values given, so answer will very likely be E.

1.) let d = 2 and i = 5
i/(d+2): 5/4 has a remainder of 1.
i/(d): 5/2 has a remainder of 1.

However, let d = 5 and i = 2
i/(d+2): 2/7 has a remainder of 2
i/(d): 2/5 has a remainder of 2

As we are asked for a specific value INSUFFICIENT

2.) let d = 2 and i = 10
i/(d+2): 10/4 quotient is 2 (d)

let d = 1 and i = 4
i/(d+2): 4/3 quotient is 1 (d)

Multiple possibilities work INSUFFICIENT

Together: Still cannot arrive to a single value for i

ANSWER E
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Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] New post   15 May 2021, 04:16
Asked: If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(d+2) m + r = d * n + r = i where m & n are integers
(d+2)m = dn
There are too many unknowns to determine value of i.
NOT SUFFICIENT

(2) The quotient when i is divided by (d+2) is d
d ( d+2) + r = i
where r < d
The equation does not give enough information to find out value of i uniquely
Let us take d = 2; d ( d+2) = 6 = i-r ;
r = {0,1}
Therefore i={5,6}
But if we take d = 3; d(d+2) = 12 = i-r
r = {0,1,2}
I= {12.11.10}
NOT SUFFICIENT

(1) + (2)
(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(d+2) m + r = d * n + r = i where m & n are integers
(d+2)m = dn
(2) The quotient when i is divided by (d+2) is d
d ( d+2) + r = i
d(d+2) = (d+2)m = dn = i - r
m = d
n = d+2
The equations combined do not give enough information to find out value of i uniquely
Let us take d = 2; d ( d+2) = 6 = i-r ;
r = {0,1}
Therefore i={5,6}
But if we take d = 3; d(d+2) = 12 = i-r
r = {0,1,2}
I= {12.11.10}
NOT SUFFICIENT

IMO E
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Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] New post   31 May 2021, 22:30
all the statements individually would provide 1, 3 and 2,4 as possiblities (maybe even an infinite number of other possiblities too ) even they are combined these possiblities aren't eliminated hence the answer IMO E
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Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink]
31 May 2021, 22:30
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