Last visit was: 27 Apr 2026, 05:33 It is currently 27 Apr 2026, 05:33
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
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,894
 [5]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,894
 [5]
If P = 177^x * 2487^y, where x and y are positive 28 Mar 2017, 11:07
1
Kudos
Add Kudos
4
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:

56% (02:09) correct 44% (02:24) wrong based on 171 sessions

History

Date
Time
Result
Not Attempted Yet
Q.
If \(P = 177^x * 2487^y\), where \(x\) and \(y\) are positive integers, what is the units digit of \(P\)?

    1. \(y = 7\)
    2. \(2x^2 + 4xy = 18 - 2y^2\)


A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.



Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

ShowHide Answer
Official Answer
B
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,894
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,894
If P = 177^x * 2487^y, where x and y are positive Updated on: 31 Mar 2017, 03:22
Originally posted by EgmatQuantExpert on 28 Mar 2017, 11:07.
Last edited by EgmatQuantExpert on 31 Mar 2017, 03:22, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The official solution has been posted. Looking forward to a healthy discussion..:)
User avatar
kris19
User avatar
Joined: 24 Sep 2014
Last visit: 19 Feb 2023
Posts: 70
Own Kudos:
125
Given Kudos: 261
Concentration: General Management, Technology
Posts: 70
Kudos: 125
If P = 177^x * 2487^y, where x and y are positive 29 Mar 2017, 04:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
s1: y = 7, it gives the units digit of 2487^y as 3, but P's units digit will vary with 177^x units digit, hence not sufficient, since x is not given
s2: this can simplified as \((\sqrt{2}x+\sqrt{2}y)^2=18\), and since x and y are positive, then x+y = 3, so x can be 1 or 2, hence the units digit of P will be 3 (i.e., 177^2x2487^1 or 177^1x2487^2)
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,894
 [1]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,894
 [1]
If P = 177^x * 2487^y, where x and y are positive 31 Mar 2017, 03:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution



Steps 1 & 2: Understand Question and Draw Inferences

We are given that:
    • \(P = 177^x * 2487^y\)
    • And we are asked to find the units digit of \(P\)
    • To find the units digit of \(P\), we need to focus on the rightmost digit of \(P\), which is its units digit.
      o So \(P = 177^x * 2487^y\)
      o Units digit of \(P\) = Units digits of (\(7^x * 7^y\))
      o Units digit of \(P\) = Units digits of \(7^{(x+y)}\)
    • Thus, we can conclude that if we can find the \(x+y\) or the individual value of x and y, we can find the units digit of P.
    • Now let us analyse each of the statements.

Step 3: Analyze Statement 1 independently

    • Statement 1 states that \(y = 7\)
    • From the first statement we get the value of only \(y\) and NOT \(x\).
    • Hence statement 1 is not sufficicent to answer the question.


Step 4: Analyze Statement 2 independently

    • Statement 2 states that \(2x^2 + 4xy = 18 - 2y^2\)
    • After simplifying we get,
      o \(x^2 + 2xy +y^2 = 9\)
      o \((x+y)^2 = 9\)
      o Since \(x\) and \(y\) are both positive, \(x+y\) will also be positive.
      o Hence, \((x+y) = 3\).
    • Now that we have the value of \(x+y\), we can find the untis digit of \(P\).
    • Hence statement 2 is sufficient to answer the question.
    • And the correct answer is Option B.



Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,894
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,894
If P = 177^x * 2487^y, where x and y are positive 31 Mar 2017, 03:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
krishna19
s1: y = 7, it gives the units digit of 2487^y as 3, but P's units digit will vary with 177^x units digit, hence not sufficient, since x is not given
s2: this can simplified as \((\sqrt{2}x+\sqrt{2}y)^2=18\), and since x and y are positive, then x+y = 3, so x can be 1 or 2, hence the units digit of P will be 3 (i.e., 177^2x2487^1 or 177^1x2487^2)
Show more


Hey Krishna,

Finding the individual value of x and y was not necessary, so no need to take x =1 and y = 2 or vice versa. Just apply exponents and write it directly as \(7^{(x+y)}\) and since we have the value of x+y, we can get our answer from the second statement. :)


Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

User avatar
stne
User avatar
Joined: 27 May 2012
Last visit: 26 Apr 2026
Posts: 1,811
Own Kudos:
2,093
 [1]
Given Kudos: 681
Posts: 1,811
Kudos: 2,093
 [1]
If P = 177^x * 2487^y, where x and y are positive 18 May 2024, 12:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert

Solution



Steps 1 & 2: Understand Question and Draw Inferences

We are given that:
    • \(P = 177^x * 2487^y\)
    • And we are asked to find the units digit of \(P\)
    • To find the units digit of \(P\), we need to focus on the rightmost digit of \(P\), which is its units digit.
      o So \(P = 177^x * 2487^y\)
      o Units digit of \(P\) = Units digits of (\(7^x * 7^y\))
      o Units digit of \(P\) = Units digits of \(7^{(x+y)}\)
    • Thus, we can conclude that if we can find the \(x+y\) or the individual value of x and y, we can find the units digit of P.
    • Now let us analyse each of the statements.

Step 3: Analyze Statement 1 independently

    • Statement 1 states that \(y = 7\)
    • From the first statement we get the value of only \(y\) and NOT \(x\).
    • Hence statement 1 is not sufficicent to answer the question.


Step 4: Analyze Statement 2 independently

    • Statement 2 states that \(2x^2 + 4xy = 18 - 2y^2\)
    • After simplifying we get,
      o \(x^2 + 2xy +y^2 = 9\)
      o \((x+y)^2 = 9\)
      o Since \(x\) and \(y\) are both positive, \(x+y\) will also be positive.
      o Hence, \((x+y) = 3\).
    • Now that we have the value of \(x+y\), we can find the untis digit of \(P\).
    • Hence statement 2 is sufficient to answer the question.
    • And the correct answer is Option B.



Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

Show more

In GMAT the DS statements should never contradict each other

According to statement 1 \(: y =7 \)
According to statement 2: \(x+y = 3\)

Using 1 and 2 :

\(x=-4 \)

This contradicts the question which says \(x\) and \(y\) are positive integers.

Perhaps if \(y\) were \(1\) or \(2\) question would not violate its own conditions! 

Hence I believe his question needs some introspection. Kindly let me know if I missed anything. Thank you.
­
Moderators:
Bunuel
Math Expert
109928 posts
kingbucky
498 posts
Gmat860sanskar
212 posts