The integers r, s ans t all have the same remainder when divided by 5. What is the value of t ?
1) r+s=t
2) 20 <= t <= 24
any method to solve this one ? Thanks
Integers r, s and t
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Since r, s, and t all have a remainder of R when divided by 5, they must ALL be contained in ONE of the following lists:yass20015 wrote:The integers r, s and t all have the same remainder when divided by 5. What is the value of t ?
1) r+s=t
2) 20 ≤ t ≤ 24
Case 1: R=0
0, 5, 10, 15, 20, 25...
Case 2: R=1
1, 6, 11, 16, 21, 26...
Case 3: R=2
2, 7, 12, 17, 22, 27...
Case 4: R=3
3, 8, 13, 18, 23, 28...
Case 5: R=4
4, 9, 14, 19, 24, 29...
Statement 1: r+s = t
Only Case 1 is viable.
No combination of values from the remaining cases will satisfy the constraint that r+s = t.
In Case 1, it's possible that r=5. s=5, and t=10.
In Case 1, it's possible that r=5, s=10, and t=15.
Since t can take on different values, INSUFFICIENT.
Statement 2: 20 ≤ t ≤ 24
In Case 1, it's possible that t=20.
In Case 2, it's possible that t=21.
Since t can take on different values, INSUFFICIENT.
Statements combined:
Only one value in Case 1 satisfies the constraint that t is between 20 and 24, inclusive: t=20.
SUFFICIENT.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.
The integers r, s ans t all have the same remainder when divided by 5. What is the value of t ?
1) r+s=t
2) 20 <= t <= 24
In the original condition, we have 3 variables (r,s,t) and 1 equation (that the remain is the same) thus we need 2 more equations to match the number of variables. Since we have 1 in each 1) and 2), C is likely the answer.
In actual calculation, r=s= multiple of 5, and t=20 which makes them unique and thus the conditions are sufficient. Therefore the answer is C
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
l Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
The integers r, s ans t all have the same remainder when divided by 5. What is the value of t ?
1) r+s=t
2) 20 <= t <= 24
In the original condition, we have 3 variables (r,s,t) and 1 equation (that the remain is the same) thus we need 2 more equations to match the number of variables. Since we have 1 in each 1) and 2), C is likely the answer.
In actual calculation, r=s= multiple of 5, and t=20 which makes them unique and thus the conditions are sufficient. Therefore the answer is C
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
l Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Let's say that the remainder is x. This means that
r = 5*something + x
s = 5*something else + x
t = 5*something else again + x
We can write this algebraically as
r = 5k + x
s = 5m + x
t = 5n + x
where k, m, and n are integers whose values we don't care about.
S1 tells us that
r + s = t, or
5k + x + 5m + x = 5n + x, or
5*(k + m) + 2x = 5n + x
In other words, 5*(something) + 2x = 5*(something else) = x, which means that 2x and x represent the same remainder! If x = 0, this works, but if x = 1, 2, 3, or 4, it doesn't. (2*1 = remainder 2, 2*2 = remainder 4, 2*3 = remainder 1, and 2*4 = remainder 3.)
So we know that r, s, and t all have remainder 0 when divided by 5; in other words, they're all multiples of 5. This is close, but no cigar: NOT SUFFICIENT.
S2:: By itself, obviously unhelpful.
Together, we know that t is a multiple of 5 between 20 and 24, inclusive, so t must be 20. Sufficient!
r = 5*something + x
s = 5*something else + x
t = 5*something else again + x
We can write this algebraically as
r = 5k + x
s = 5m + x
t = 5n + x
where k, m, and n are integers whose values we don't care about.
S1 tells us that
r + s = t, or
5k + x + 5m + x = 5n + x, or
5*(k + m) + 2x = 5n + x
In other words, 5*(something) + 2x = 5*(something else) = x, which means that 2x and x represent the same remainder! If x = 0, this works, but if x = 1, 2, 3, or 4, it doesn't. (2*1 = remainder 2, 2*2 = remainder 4, 2*3 = remainder 1, and 2*4 = remainder 3.)
So we know that r, s, and t all have remainder 0 when divided by 5; in other words, they're all multiples of 5. This is close, but no cigar: NOT SUFFICIENT.
S2:: By itself, obviously unhelpful.
Together, we know that t is a multiple of 5 between 20 and 24, inclusive, so t must be 20. Sufficient!