If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1, then

Expert replies

Previous Topic Next Topic

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun Jun 14, 2020 8:30 am

Timer

00:00

Your answer

Difficulty–

right wrong

Pick an answer to see how members did

If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1, then what is the least possible sum of $a$ and $b?$

A. 2
B. 7
C. 17
D. 24
E. 26

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Sun Jun 14, 2020 8:30 am

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

Re: If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1,

by Jay@ManhattanReview » Mon Jun 15, 2020 9:17 pm

M7MBA wrote: ↑
Sun Jun 14, 2020 8:30 am
If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1, then what is the least possible sum of $a$ and $b?$

A. 2
B. 7
C. 17
D. 24
E. 26

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Observing $7(a - 1) = 17(b - 1),$ we find that 7 and 17 are co-prime to each other; thus, we have $(a - 1) = 17=> a = 18$ and $7=(b - 1)=b=8$

So, the least possible sum of $a$ and $b$ = 18 + 8 = 26

Correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: ACT Classes | ACT Tutoring | IELTS Tutoring | GMAT Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1,

by swerve » Tue Jun 16, 2020 4:26 am

M7MBA wrote: ↑
Sun Jun 14, 2020 8:30 am
If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1, then what is the least possible sum of $a$ and $b?$

A. 2
B. 7
C. 17
D. 24
E. 26

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Two numbers are equal if the expression on each side is equal to the given number on opposite side.
For e.g:

$7(a-1)=17(b-1)$

So, we have
$a-1=17$
$b-1=7$

Hence, $a=18$ and $b=8$ and $a+b=26$

gentvenus: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue Oct 01, 2019 5:49 am

Re: If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1,

by gentvenus » Tue Jun 16, 2020 8:51 am

E.
7 and 17 are co-prime to each other
Least possible sum = 18 + 8 = 26

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1,

by Scott@TargetTestPrep » Sat Jun 20, 2020 1:56 pm

M7MBA wrote: ↑
Sun Jun 14, 2020 8:30 am
If $7(a - 1) = 17(b - 1),$ and $a$ and $b$ are both positive integers the product of which is greater than 1, then what is the least possible sum of $a$ and $b?$

A. 2
B. 7
C. 17
D. 24
E. 26

[spoiler]OA=E[/spoiler]

Solution:

Since a and b are positive integers and ab > 1, then a and b are both greater than 1.
Since 7 and 17 do not have any common factors other than 1, we see that a - 1 must be divisible by 17 and b -1 must be divisible by 7. So a and b are both greater than 1, we need a - 1 = 17 and b - 1 = 7 in order to have the least possible sum of a and b. In that case, a = 18 and b = 8, and their sum is 26.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Featured schoolRound 2 closes Jan 7, 2027 54 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review