Last visit was: 29 Apr 2026, 19:37 It is currently 29 Apr 2026, 19:37
Home
Messages
Tests
Schools
Events
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Russ19
User avatar
Joined: 29 Oct 2019
Last visit: 18 Mar 2026
Posts: 1,339
Own Kudos:
1,988
 [2]
Given Kudos: 582
Posts: 1,339
Kudos: 1,988
 [2]
If p is a positive integer less than 70, and 71^2 − 142p + p^2 is divi 24 Sep 2021, 05:46
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

58% (02:13) correct 42% (02:26) wrong based on 124 sessions

History

Date
Time
Result
Not Attempted Yet
If \(p\) is a positive integer less than\( 70\), and \(71^2 − 142p + p^2\) is divisible by \(49\), what is the remainder when \(p\) is divided by \(7\)?

A) 0

B) 1

C) 2

D) 4

E) 6
ShowHide Answer
Official Answer
B
User avatar
rishabh195
User avatar
Joined: 06 Sep 2021
Last visit: 05 Jul 2025
Posts: 15
Own Kudos:
2
Given Kudos: 118
Posts: 15
Kudos: 2
If p is a positive integer less than 70, and 71^2 − 142p + p^2 is divi 24 Sep 2021, 06:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sjuniv32
If \(p\) is a positive integer less than\( 70\), and \(71^2 − 142p + p^2\) is divisible by \(49\), what is the remainder when \(p\) is divided by \(7\)?

A) 0

B) 1

C) 2

D) 4

E) 6
Show more


I am not getting the answer as B. Please help

I am getting the value of p as 70, but because the value of p is less than 70..... I took it as 69 and when 69 divided by 7, it gives a remainder of 6.

But as per the OA, it should give the remainder of 1.

Where am I going wrong? Please help

Posted from my mobile device
User avatar
PyjamaScientist
User avatar
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Last visit: 04 Apr 2026
Posts: 1,125
Own Kudos:
1,358
Given Kudos: 633
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Products:
My Reviews
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Posts: 1,125
Kudos: 1,358
If p is a positive integer less than 70, and 71^2 − 142p + p^2 is divi 24 Sep 2021, 08:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rishabh195
sjuniv32
If \(p\) is a positive integer less than\( 70\), and \(71^2 − 142p + p^2\) is divisible by \(49\), what is the remainder when \(p\) is divided by \(7\)?

A) 0

B) 1

C) 2

D) 4

E) 6


I am not getting the answer as B. Please help

I am getting the value of p as 70, but because the value of p is less than 70..... I took it as 69 and when 69 divided by 7, it gives a remainder of 6.

But as per the OA, it should give the remainder of 1.

Where am I going wrong? Please help

Posted from my mobile device
Show more

How are you getting the value of P as 70, can you explain?


Here's how I went about it-

Given: 71^2 - 142p + p^2 is divisible by 49, which means, 71^2 - 142p + p^2 = 49k ---------(1)

If you rearrange 71^2 - 142p + p^2 , you can write it in the form of (a-b)^2.
That will be- (71 - p)^2

Using (1) above,
(71 - p)^2 = 49k
49k can be written as (7K)^2. Since the left side of the equation is a perfect square, the right side should be also a perfect square.

Equating both sides, you would get->

-> 71 - p = 7K
-> p = 71 - 7k

Now, the question is, what is the remainder when p is divided by 7.

-> 71/7 - 7K/7. Here, 7K/7 would yield no remainder. But 71/7 would yield a remainder of 1.

Hence, the option B is correct.
User avatar
SaquibHGMATWhiz
User avatar
GMATWhiz Representative
Joined: 23 May 2022
Last visit: 12 Jun 2024
Posts: 623
Own Kudos:
779
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Expert
Expert reply
GMAT 1: 760 Q51 V40
Posts: 623
Kudos: 779
If p is a positive integer less than 70, and 71^2 − 142p + p^2 is divi 12 Jul 2023, 06:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Russ19
If \(p\) is a positive integer less than\( 70\), and \(71^2 − 142p + p^2\) is divisible by \(49\), what is the remainder when \(p\) is divided by \(7\)?

A) 0
B) 1
C) 2
D) 4
E) 6
Show more

Solution:
  • According to the question, \(p\) is a positive integer less than \(70\)
  • And \(71^2 − 142p + p^2=49k\) where k is an integer
    \(⇒(71-p)^2=49k\)
    \(⇒71-p=7\sqrt{k}\)
    \(⇒p=71-7\sqrt{k}\)
  • Remainder when \(p\) is divided by \(7=(\frac{71-7\sqrt{k}}{7})_r=(\frac{71}{7})_r-(\frac{7\sqrt{k}}{7})_r=1-0=1\)

Hence the right answer is Option B
Moderators:
Bunuel
Math Expert
109975 posts
Krunaal
Tuck School Moderator
852 posts