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

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If i and d are integers, what is the value of i? [#permalink] New post 26 May 2011, 19:25
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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

What is the best way to tackle this kind of DS problems?
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Feb 2012, 06:32, edited 1 time in total.
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Re: What is the best way to tackle this kind of DS problems [#permalink] New post 07 Feb 2012, 06:31
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smodak 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

What is the best way to tackle this kind of DS problems?


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: What is the best way to tackle this kind of DS problems [#permalink] New post 13 May 2014, 15:12
Bunuel wrote:
smodak 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

What is the best way to tackle this kind of DS problems?


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.


What's the trick in this question? Is it only the fact that 'd' and 'd+2' as denominators can be larger than 'i' and therefore, 'i' could take any value as long as it is smaller than the denominator as well as being a multiple of both 'd' and 'd+2' ? (Has to be a multiple otherwise remainder can't be zero)

What do you guys thimk?

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Re: What is the best way to tackle this kind of DS problems [#permalink] New post 30 May 2014, 05:07
Bunuel wrote:
smodak 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

What is the best way to tackle this kind of DS problems?


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.


Can this somehow be done algebraically or conceptually

I had that first i/ (d+2) and i/d, yield the same remainder, but if both d and d+2, are larger than i, then 'i' could just take any value as the remainder.

Clearly insufficient

Statement 2 we have that i = (d)(d+2) + r

Now, if we replace in first term, we have that (d)(d+2) + r / (d+2), gives d as quotient but still we are left with r as a remainder of d+2. while we also know that i/d gives the same remainder. Here we learn that 'i' must be greater than d+2 since if gives quotient d. However, we still have no clue as to what remainder the division can yield

Both together, i>d, i = d(d+2) + r, and 'r' here is equal to the remainder of i/d = d(d+2) / d.

So r/d = r/d+2, but still no information on the remainder

Hence answer is E
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If i and d are integers, what is the value of i? [#permalink] New post 17 Jun 2014, 13:38
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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Re: If i and d are integers, what is the value of i? [#permalink] New post 17 Jun 2014, 13:57
Expert's post
goodyear2013 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


Merging similar topics. Please refer to the discussion above.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If i and d are integers, what is the value of i? [#permalink] New post 17 Jun 2014, 21:05
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smodak 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

What is the best way to tackle this kind of DS problems?


Question: What is the value of i?

How do you express stmnt 1 in an equation?
Stmnt 1: The remainder when i is divided by (d+2) is the same as when i is divided by d.

Say when i is divided by d or d + 2, the remainder we obtain is r. Does this mean that if we subtract r from i, whatever is leftover will be divisible by d as well as (d+2)? So assuming that d and d+2 do not have any common factors (even if they do have common factors other than 1, they can only have 2 as a common factor), we can put it down as

i - r = d(d + 2)k
i = d(d + 2)k + r
Now for different values of d, k and r, values of i will be different.

Stmnt 2: The quotient when i is divided by (d+2) is d
This tells us that
i = d(d +2) + r
Now for different values of d and r, values of i will be different.

Using both, we know that k is 1. But for different values of d and r, we can still have different values of i. Not sufficient.

Answer (E)

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Re: If i and d are integers, what is the value of i?   [#permalink] 17 Jun 2014, 21:05
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