Last visit was: 17 Jul 2025, 11:47 It is currently 17 Jul 2025, 11:47
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
555-605 Level|   Algebra|   Inequalities|      
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,681
Own Kudos:
19,471
 [5]
Given Kudos: 165
Expert
Expert reply
Posts: 3,681
Kudos: 19,471
 [5]
The decimal representation of the number is given 23 May 2017, 07:26
1
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

74% (02:16) correct 26% (02:12) wrong based on 234 sessions

History

Date
Time
Result
Not Attempted Yet
Q.

\(\sqrt{z}/4 = a.bc\)

The decimal representation of the number is given above, where z is a positive number and a, b and c are single-digit non-negative integers. Is a = 0?

1. \(\frac{z^2}{4} > 64\)

2. \(\frac{z^{0.25}}{4}> 2\)

Answer Choices



    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.
ShowHide Answer
Official Answer
D
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,681
Own Kudos:
19,471
Given Kudos: 165
Expert
Expert reply
Posts: 3,681
Kudos: 19,471
The decimal representation of the number is given Updated on: 31 May 2017, 05:11
Originally posted by EgmatQuantExpert on 23 May 2017, 07:26.
Last edited by EgmatQuantExpert on 31 May 2017, 05:11, 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
quantumliner
User avatar
Joined: 24 Apr 2016
Last visit: 26 Sep 2018
Posts: 244
Own Kudos:
753
Given Kudos: 48
Posts: 244
Kudos: 753
The decimal representation of the number is given 23 May 2017, 10:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1: . (z^2)/4>64
Given that z is positive, lets take the square root of both the sides, we get

z/2 >8, which can written as z >16.

Taking square root of both sides again, we get

(z^1/2) > 4, dividing both sides by 4, we get, (z^1/2)/4 > 1. So a is not equal to 0. This statement is sufficient.

Statement 2: (z^1/4)/4 > 2

Squaring both sides we get, (z^1/2)/16 > 4, this can be written as

(z^1/2)/4 > 16
.
(z^1/2) > 64. So a is not equal to 0. This statement is sufficient.

Answer is D
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,681
Own Kudos:
19,471
Given Kudos: 165
Expert
Expert reply
Posts: 3,681
Kudos: 19,471
The decimal representation of the number is given 31 May 2017, 05:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Official Solution




Steps 1 & 2: Understand Question and Draw Inferences

Given:

    \(\sqrt{z}/4 = a.bc\)

    \(z > 0\)

    a, b, c = {0, 1, 2, 3 . . . 8, 9}

To find: Is a = 0?

    The answer is YES if \(\sqrt{z}/4\) < 1

    That is, if \(\sqrt{z}< 4\)

    Since \(\sqrt{z}\) is positive, the sign of inequality will remain the same upon squaring both sides

    So, the answer is YES if z < 16

    Else, the answer is NO


Step 3: Analyze Statement 1 independently

(1) \(\frac{z^2}{4} > 64\)

Multiplying the above inequality by 4 we get:

    \(z^2 > 64*4\)

Taking square roots we get

    z > 8 * 2 (Ignore negative roots as z is given as positive number)
    z > 16
    So, z is not less than 16

So, the answer is NO

Statement 1 is sufficient to answer the question



Step 4: Analyze Statement 2 independently

(2) ​\(\frac{z^{0.25}}{4}> 2\)


Since \(z^{0.25}\) is positive, squaring both sides twice will not change the sign of inequality:

    \(z^{0.25*4} > 8^4\)

    \(z > 2^{12}\)

So, z is not less than 16

Thus, the answer is NO


Statement 2 is sufficient to answer the question


Answer: Option D


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 :)

User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 17 Jul 2025
Posts: 4,145
Own Kudos:
10,635
 [1]
Given Kudos: 98
 Q51  V47
Expert
Expert reply
Posts: 4,145
Kudos: 10,635
 [1]
The decimal representation of the number is given 20 Nov 2020, 08:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert
Q.

\(\sqrt{z}/4 = a.bc\)

The decimal representation of the number is given above, where z is a positive number and a, b and c are single-digit non-negative integers. Is a = 0?

1. \(\frac{z^2}{4} > 64\)

2. \(\frac{z^{0.25}}{4}> 2\)

From Statement 1, if z^2/4 > 64, then z^2 > (4)(64), and z > (2)(8), so z > 16. So √z/4 is thus greater than 1, and a cannot be zero, and Statement 1 is sufficient.

From Statement 2, z^(1/4) > 8, so z > 8^4. Then √z/4 is greater than √(8^4)/4 = 16, and the decimal representation of √z/4 cannot possibly look like "a.bc". So I have no idea how to now answer the question: is "a" the units digit in the decimal representation of √z/4? If so, then a can certainly equal zero. But if instead the question meant to say that a is the integer part of √z/4, then clearly a is greater than zero.

So it's impossible to answer the question, but the answer is A or D depending on what one guesses it means.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,437
Own Kudos:
1,013
Posts: 37,437
Kudos: 1,013
The decimal representation of the number is given 28 Feb 2023, 09:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
102603 posts
kingbucky
453 posts