GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Dec 2018, 13:53

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If [z] denotes the least integer greater

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2313
If [z] denotes the least integer greater  [#permalink]

Show Tags

New post 24 May 2017, 10:50
2
13
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:43) correct 49% (01:49) wrong based on 234 sessions

HideShow timer Statistics

Q.

If [z] denotes the least integer greater than or equal to z and [\(z^2\)] = 2, which of the following could be the value of [z]?

    I. 2
    II. 1
    III. -2


Answer Choices



    A. I only
    B. II only
    C. III only
    D. I and II only
    E. II and III only

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 331
If [z] denotes the least integer greater  [#permalink]

Show Tags

New post 24 May 2017, 13:13
\([z^2] = 2\) means that

\(1<z^2\leq{2}\)

Now, Taking Square Root of both the sides.

If Z is positive, then

\(1<z\leq{\sqrt{2}}\)

then [z] = 2

If Z is negative, then

\(-1>z\geq{-\sqrt{2}}\)

then [z] = -1

Answer is A. I only
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: If [z] denotes the least integer greater than or equal to z and [z2] =  [#permalink]

Show Tags

New post 25 May 2017, 13:05
1
1
niteshwaghray wrote:
If [z] denotes the least integer greater than or equal to z and [\(z^2\)] = 2, which of the following could be the value of [z]?

I) 2
II) 1
III) -2


A. I only
B. II only
C. III only
D. I and II only
E. II and III only


Given function rounds up a number to the nearest integer. For example, [1.3] = 2, because 2 is the least integer greater than or equal to 1.3.

[\(z^2\)] = 2;

\(1 < z^2 \leq 2\);

\(1 <|z| \leq \sqrt{2}\) (\(\sqrt{2} \approx 1.4\)).

\(1 < z \leq \sqrt{2}\) or \(-1 > z \geq \sqrt{2}\)

[z] can be 2 (if \(1 < z \leq \sqrt{2}\)) or -1 (if \(-1 > z \geq \sqrt{2}\)).

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2313
Re: If [z] denotes the least integer greater  [#permalink]

Show Tags

New post 31 May 2017, 05:09
2
1

Official Solution



Given:

    • The function [z]
    • \([z^2] = 2\)

To find: Can [z] be {2, 1, -2}?

Approach:

    • To find which values of [z] are possible and which are not, we need to first know the range of possible values of z. Once we know what z can be, we’ll be able to find what [z] can be.

We’ll get an idea of the possible values of z from the fact that \([z^2] = 2\)

Working Out:

    • \([z^2] = 2\)

    • This means the least integer that is greater than or equal to \(z^2\) is 2.


    • We can write: \(1 < z^2 ≤ 2\)

    • The above inequality contains 2 inequalities: \(z^2 > 1\) AND \(z^2 ≤ 2\)
So now, we’ll solve these inequalities one by one, and then find the values of z that satisfy both these inequalities

    • Solving \(z^2 > 1\)

    • \(z^2 – 1 > 0\)

    • \((z+1)(z-1) > 0\)

This means, \(z < - 1\) or \(z > 1\) . . . (1)

    • Solving \(z^2 ≤ 2\)

    • \(z^2 – 2 ≤ 0\)

    • \((z + √2)(z-√2) ≤ 0\)

That is, \(-√2 ≤ z ≤ √2\) . . . (2)

Combining (1) and (2):

Combining them to find their overlap zones and finding those values of z that satisfy both the inequalities

    • So, either \(-√2 ≤ z < -1\) or \(1 < z ≤ √2\)

      • Either \(-√2 ≤ z < -1\)

      • \(-1.4  ≤ z < -1\)

    • In this case, \([z] = -1\)

      • Or \(1 < z ≤ √2\)

      • \(1 < z ≤ 1.4 \)

    • \([z] = 2\)
Thus, we see that [z] is either equal to -1 or equal to 2. Out of the 3 given values, only value I (which is 2) is therefore possible.

Looking at the answer choices, we see that the correct answer is Option A


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 :)

Image
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
User avatar
G
Joined: 03 Mar 2018
Posts: 201
Premium Member CAT Tests
If [z] denotes the least integer greater than or equal to z and [z^2]  [#permalink]

Show Tags

New post 05 Mar 2018, 06:01
If [z] denotes the least integer greater than or equal to z and [z^2] = 2, which of the following could be the value of [z]?

I. 2
II. 1
III. -2

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) II and III only
_________________

Please mention my name in your valuable replies.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7107
Re: If [z] denotes the least integer greater than or equal to z and [z^2]  [#permalink]

Show Tags

New post 05 Mar 2018, 06:25
1
itisSheldon wrote:
If [z] denotes the least integer greater than or equal to z and [z^2] = 2, which of the following could be the value of [z]?

I. 2
II. 1
III. -2

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) II and III only



Good question...
if [z^2] =2, \(z^2\) lies between 2 and 3
therefore z lies between \(\sqrt{2}=1.4\) and \(\sqrt{3}=1.7\) or between \(-\sqrt{2}=-1.4\) and \(-\sqrt{3}=-1.7\) if z is negative..
so when z is positive it lies between 1.4 and 1.7 and the NEXT greater integer is 2 so [z]=2
but when z is negative it lies between -1.4 and -1.7 and the NEXT greater integer is -1 so [z]=-1.. Be careful here and do not take -2

Only 2 is given
ans A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: If [z] denotes the least integer greater  [#permalink]

Show Tags

New post 05 Mar 2018, 06:30
itisSheldon wrote:
If [z] denotes the least integer greater than or equal to z and [z^2] = 2, which of the following could be the value of [z]?

I. 2
II. 1
III. -2

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) II and III only


Merging topics. Please search before posting. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: If [z] denotes the least integer greater &nbs [#permalink] 05 Mar 2018, 06:30
Display posts from previous: Sort by

If [z] denotes the least integer greater

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.