Events & Promotions
|
|
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.
Apr 3001:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2912:30 AM EDT
-01:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
May 0306:30 AM PDT
-08:30 AM PDT
Verbal trouble on GMAT? Fix it NOW! Join Sunita Singhvi for a focused webinar on actionable strategies to boost your Verbal score and take your performance to the next level.
02 Aug 2021, 03:15
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
94% (01:30) correct
6%
(01:42)
wrong
based on 150
sessions
History
Date
Time
Result
Not Attempted Yet
The difference between a two-digit number and the number obtained by interchanging the digits is 18. The sum of the digits is 10 and the digit at the ten’s place is bigger than the digit at the unit’s place, What is the two-digit number?
(A) 28
(B) 46
(C) 64
(D) 73
(E) 82
(A) 28
(B) 46
(C) 64
(D) 73
(E) 82
02 Aug 2021, 03:20
Kudos
Bookmarks
Explanation:
10x+y - 10y - x = 18
9x - 9y = 18
x-y = 2 --- Eqn 1
x+y = 10 --- Eqn 2
From Eqn 1 & 2,
2x = 12
x = 6
y = 4
number = 64
IMO-C
10x+y - 10y - x = 18
9x - 9y = 18
x-y = 2 --- Eqn 1
x+y = 10 --- Eqn 2
From Eqn 1 & 2,
2x = 12
x = 6
y = 4
number = 64
IMO-C
02 Aug 2021, 04:41
Kudos
Bookmarks
Solution:
Let us assume a two-digit number be \(10x+y\). Where \(x\) and \(y\) are ten's and unit's digit respectively.
And the number obtained by interchanging the digits will be \(= 10y+x\).
We are given that their difference is \(18\). Thus we can say \(10x+y-(10y+x)=18\)
\(⇒ 10x+y-10y-x=18\)
\(⇒ 9x-9y=18\)
\(⇒ 9(x-y)=18\)
\(⇒ x-y=\frac{18}{9}\)
\(⇒ x-y=2\)..... \((i)\)
We are given that the sum of the digits is \(10\). Thus we can say \(x+y=10\)..... \((ii)\)
Adding \(eq(i)\) and \(eq(ii)\), we get: \(x-y+x+y=2+10\)
\(⇒ 2x=12\)
\(⇒ x=\frac{12}{2}\)
\(⇒ x=6\)
Plugging \(x=6\) in equation \((i)\), we get \(x-y=2\)
\(⇒ 6-y=2\)
\(⇒ y=6-2\)
\(⇒ y=4\)
We have both the digits now. Thus the number \(= 10x+y=10\times 6+4=64\)
Hence the right answer is Option C.
Let us assume a two-digit number be \(10x+y\). Where \(x\) and \(y\) are ten's and unit's digit respectively.
And the number obtained by interchanging the digits will be \(= 10y+x\).
We are given that their difference is \(18\). Thus we can say \(10x+y-(10y+x)=18\)
\(⇒ 10x+y-10y-x=18\)
\(⇒ 9x-9y=18\)
\(⇒ 9(x-y)=18\)
\(⇒ x-y=\frac{18}{9}\)
\(⇒ x-y=2\)..... \((i)\)
We are given that the sum of the digits is \(10\). Thus we can say \(x+y=10\)..... \((ii)\)
Adding \(eq(i)\) and \(eq(ii)\), we get: \(x-y+x+y=2+10\)
\(⇒ 2x=12\)
\(⇒ x=\frac{12}{2}\)
\(⇒ x=6\)
Plugging \(x=6\) in equation \((i)\), we get \(x-y=2\)
\(⇒ 6-y=2\)
\(⇒ y=6-2\)
\(⇒ y=4\)
We have both the digits now. Thus the number \(= 10x+y=10\times 6+4=64\)
Hence the right answer is Option C.
