by: PaceMile
14 mins
by: hd29
17 mins
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:10) correct
22%
(01:29)
wrong
based on 3698
sessions
History
Date
Time
Result
Not Attempted Yet
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.
_________________
(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.
Solving this question helps.
Taking a timed set of similar questions in
GMAT Club Forum Quiz →
is even better.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
SOLUTION
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30 --> \(x=100q+30\), so \(x\) can be: 30, 130, 230, ... Each has the tens digit of 3. Sufficient.
(2) x divided by 110 has a remainder of 30 --> \(x=110p+30\), so \(x\) can be: 30, 250, ... We already have two values for the tens digit. Not sufficient.
Answer: A.
_________________
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30 --> \(x=100q+30\), so \(x\) can be: 30, 130, 230, ... Each has the tens digit of 3. Sufficient.
(2) x divided by 110 has a remainder of 30 --> \(x=110p+30\), so \(x\) can be: 30, 250, ... We already have two values for the tens digit. Not sufficient.
Answer: A.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
St 1: Sufficient: X should be number such as 130, 230, 330, 430.... In all case if we divide X by 100 the remainder is 30. so the tens digit is 3
St 2: Insufficient: Let say X be 140 : In this case the remainder is 30 when divided by 110, So tens digit is 4
Let say X be 250: In this case the remainder is 30 when divided by 110, So tens digit is 5.
Hence answer A
St 2: Insufficient: Let say X be 140 : In this case the remainder is 30 when divided by 110, So tens digit is 4
Let say X be 250: In this case the remainder is 30 when divided by 110, So tens digit is 5.
Hence answer A
The best way to solve this question is to use equation rather than getting stuck in remainder part
1) x = 100a+30 , where a is non-negative integer.
Thus x can take following values 30,130,230,330....etc
So the ten's digit always will be 3
Sufficient
2) x = 110a+30 , where a is non-negative integer.
Thus x can take following values 30,140,250,380....etc
So the ten's digit in not unique
In-Sufficient
Answer A
1) x = 100a+30 , where a is non-negative integer.
Thus x can take following values 30,130,230,330....etc
So the ten's digit always will be 3
Sufficient
2) x = 110a+30 , where a is non-negative integer.
Thus x can take following values 30,140,250,380....etc
So the ten's digit in not unique
In-Sufficient
Answer A
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30.
Means, x=100n+30 ; n=1,2,3...
x can be 130,230,330-in all cases tens place is held by 3- sufficient
(2) x divided by 110 has a remainder of 30.
Means, x=110n+30 ; n =1,2,3...
x can be 110,220,330- the tens place is changing with changing value of n - insufficient
Answer : A
(1) x divided by 100 has a remainder of 30.
Means, x=100n+30 ; n=1,2,3...
x can be 130,230,330-in all cases tens place is held by 3- sufficient
(2) x divided by 110 has a remainder of 30.
Means, x=110n+30 ; n =1,2,3...
x can be 110,220,330- the tens place is changing with changing value of n - insufficient
Answer : A
Bunuel
Question
1) x divided by 100 has a remainder of 30 --> x=100q+30: 30, 130, 230, ... as you can see every such number has 3 as the tens digit. Sufficient. QUESTION :How exactly are 30, 130, 230 computed?
sagnik242
If q=0, then x=30;
If q=1, then x=130;
If q=2, then x=230;
If q=3, then x=330;
...
All these numbers when divided by 100 gives the remainder of 30.
Generally, if \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).
For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\).
Notice that \(0\leq{r}<x\) means that remainder is a non-negative integer and always less than divisor.
This formula can also be written as \(\frac{y}{x} = q + \frac{r}{x}\).
You really need to brush up fundamentals:
Theory on remainders problems: remainders-144665.html
Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html
All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199
Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html
All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199
Hope this helps.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Bunuel chetan2u niks18
amanvermagmat
Is it valid to take quotient(p/q) as 0 ? I assumed if divisor is divided by dividend, we need minimum value of quotient to be
non positive for division to be valid.
amanvermagmat
Quote:
Is it valid to take quotient(p/q) as 0 ? I assumed if divisor is divided by dividend, we need minimum value of quotient to be
non positive for division to be valid.
adkikani
What is the remainder when 30 is divided by 100? Isn't it 30? So, why could not p (or q) be 0?
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Posts: 6,727
Bunuel
Target question: What is the tens digit of positive integer x ?
Statement 1: x divided by 100 has a remainder of 30
ASIDE: When it comes to remainders, we have a 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.
In other words, the possible values of k are: 1, 6, 11, 16, 21, 26, 31, . . . etc.
So, from statement 1, we can conclude that the possible values of x are: 30, 130, 230, 330, 430, 530,. . .
In ALL possible values of x, the tens digit is always 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x divided by 110 has a remainder of 30
From statement 2, we can conclude that the possible values of x are: 30, 140, 250, 360, 470, 580,. . .
Notice that the the tens digit can have many different values
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
hello
Am i the only one thinking x as the same number which gave the answer c for me
Am i the only one thinking x as the same number which gave the answer c for me
Bunuel
Hi Bunuel,
I was wondering how do we know that x cannot be a larger number which has 4 or more digits? e.g. x=1030
in that case, the tenth digit would be 0 and neither statements would be sufficient to answer the question.
Is there any "rule of thumb" on GMAT that a positive integer only refers to a max. 3 digit number?
Could you please share your thoughts about it?
Thank you.
WaterVac
Hello to you;
1030 divided by 100 gives 30 as a remainder and number 1030 has a tens digit of 3 just like any number divided by 100 to leave a remainder of 30 will have 3 as a tens digit;so Statement A is sufficient
Bunuel
(1) \(x=100q+30; x \ can \ be 130, 230, 330\) All cases tens digit is \(3\) Sufficient.
(2) \(x=110q+30; x \ can \ be 140, 250,\) Two different tens \((4, or \ 5)\), Insufficient.
The answer is A
GMAT 1: 750 Q49 V42
Posts: 469
Moderator:
Announcements
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.