[phpBB Debug] PHP Notice: in file /viewtopic.php on line 1524: Undefined array key "topic_tags_visibility"
[phpBB Debug] PHP Notice: in file /viewtopic.php on line 1525: Undefined array key "timer_statistics_visibility"
The integers x and (x - 1) are not divisible by 4. : Quantitative Comparison Questions

Last visit was: 20 Jul 2024, 11:55 It is currently 20 Jul 2024, 11:55

Close

GRE Prep 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 GRE 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
Verbal Expert
Joined: 18 Apr 2015
Posts: 29128
Own Kudos [?]: 34165 [27]
Given Kudos: 25525
Send PM
Most Helpful Expert Reply
Verbal Expert
Joined: 18 Apr 2015
Posts: 29128
Own Kudos [?]: 34165 [10]
Given Kudos: 25525
Send PM
Most Helpful Community Reply
avatar
Intern
Intern
Joined: 27 Jan 2019
Posts: 29
Own Kudos [?]: 53 [13]
Given Kudos: 0
Send PM
General Discussion
avatar
Intern
Intern
Joined: 11 Aug 2017
Posts: 4
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
Hi,

Can you please explain the solution?
avatar
Intern
Intern
Joined: 12 Nov 2017
Posts: 30
Own Kudos [?]: 51 [0]
Given Kudos: 0
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
Couldnt x be 1 and x-1 be 0

Isnt 0 also an integer?

Carcass wrote:
This is really a tough one. Whenever you see such question there is always a pattern underlined it.

now we do know that x -1 and x are consecutive positive integers.

if you pick a number you will see the pattern

1 and 2. follow that for x/4 x = 2 which means 2/4 = 1/2 = 0.50 and the tenth digit is 5 is always greater than the zero. 5 > 0 (zero is the hundredths digit)

2 and 3. follow that for x/4 you do have 3/4 = 0.75 and 7 > 5

5 and 6. follow that for x/4 you do have 6/4 = 3/2 = 1.50 and 5 > 0

and so on and so forth this pattern.

Therefore, the tenth digit is always greater than the hundredth digit

A is the answer
Verbal Expert
Joined: 18 Apr 2015
Posts: 29128
Own Kudos [?]: 34165 [0]
Given Kudos: 25525
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
Expert Reply
No. Cannot be zero x.

Otherwise, the quantities were unuseful. if you consider x as zero (that is an integer) then in the quantities x/4 is impossible. x/0 is indefinite. And the question would fall apart.


Hope this helps
avatar
Manager
Manager
Joined: 04 Apr 2020
Posts: 90
Own Kudos [?]: 82 [2]
Given Kudos: 0
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
2
Multiples of 4 are 4 units apart each other. 4, 8, 12, 16 ...

Now x-1 and x are not multiples of 4. In a given set of 5 numbers where extremes are multiples of 4, like {4, 5, 6, 7, 8} x and x-1 are not multiples of 4. In the range, this can be 5,6 or 6,7. So x can be 5 or 6. Dividing them by 4, we get 1.50 and 1.75. In both the cases, tenth digit is greater.

Consider a second set for confirmation. {8, 9, 10, 11, 12}. x can be 10 or 11. 10/4 = 2.5 and 11/4 = 2.75. In this case too, tenth digit is greater. So the pattern repeats in every set and hence the tenth digit will ALWAYS be GREATER than the hundredth digit.

The answer is A.
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 155 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
fifan wrote:
a number that is not divisible by 4 will give either 1,2,3 as remainder. Hence when the remainder is divided by 4, the decimals we get will end in 0.25, 0.50 or 0.75. since x and x-1 are consecutive integers. this rules out 1 as reminder when x is divided by 4. E.g if x is 5 then x-1 is 4 which is divisible by 4 but not allowed by the question. So the only possibilities are 2 and 3 as remainder which give us 0.50 or 0.75 as decimals. in these decimal remainder we see that tenths digit is greater than the hundredths digit. so A is greater than B



I do not understand why you rule out the possibility of 1 as a remainder, Besides, Its seem all fine.
Intern
Intern
Joined: 29 Apr 2021
Posts: 24
Own Kudos [?]: 31 [2]
Given Kudos: 19
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
2
kumarneupane4344 wrote:
fifan wrote:
a number that is not divisible by 4 will give either 1,2,3 as remainder. Hence when the remainder is divided by 4, the decimals we get will end in 0.25, 0.50 or 0.75. since x and x-1 are consecutive integers. this rules out 1 as reminder when x is divided by 4. E.g if x is 5 then x-1 is 4 which is divisible by 4 but not allowed by the question. So the only possibilities are 2 and 3 as remainder which give us 0.50 or 0.75 as decimals. in these decimal remainder we see that tenths digit is greater than the hundredths digit. so A is greater than B



I do not understand why you rule out the possibility of 1 as a remainder, Besides, Its seem all fine.


The question says "The integers x and (x - 1) are NOT divisible by 4." If 1 is a remainder, suppose for the number 9, then x= 9, and x-1 becomes (9-1)= 8, which IS DIVISIBLE by 4.
So we have to rule out the possibility of 1 as a remainder to comply with the question.

Hope this helps!
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 155 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
:blushing: :blushing:
saumik wrote:
kumarneupane4344 wrote:
fifan wrote:
a number that is not divisible by 4 will give either 1,2,3 as remainder. Hence when the remainder is divided by 4, the decimals we get will end in 0.25, 0.50 or 0.75. since x and x-1 are consecutive integers. this rules out 1 as reminder when x is divided by 4. E.g if x is 5 then x-1 is 4 which is divisible by 4 but not allowed by the question. So the only possibilities are 2 and 3 as remainder which give us 0.50 or 0.75 as decimals. in these decimal remainder we see that tenths digit is greater than the hundredths digit. so A is greater than B



I do not understand why you rule out the possibility of 1 as a remainder, Besides, Its seem all fine.


The question says "The integers x and (x - 1) are NOT divisible by 4." If 1 is a remainder, suppose for the number 9, then x= 9, and x-1 becomes (9-1)= 8, which IS DIVISIBLE by 4.
So we have to rule out the possibility of 1 as a remainder to comply with the question.

Hope this helps!
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11874 [3]
Given Kudos: 136
Send PM
The integers x and (x - 1) are not divisible by 4. [#permalink]
3
Carcass wrote:
The integers x and (x - 1) are not divisible by 4.

Quantity A
Quantity B
The value of the tenths digit of \(\frac{x}{4}\)
The value of the hundredths digit of \(\frac{x}{4}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Sorry folks, but the correct answer is NOT A.
Since there's no information given that stipulates x must be positive, we must also consider negative values of x



The integers x and (x - 1) are not divisible by 4.
So, some possible values of x include: -6, -5, -2, -1, 2, 3, 6, 7, 10, 11, etc

Let's test a few values

If x = -6, we see that x/4 = -6/4 = -1.50. In this case, Quantity A = 5, and Quantity B = 0.
Here, Quantity A is greater than Quantity B

If x = -5, we see that x/4 = -5/4 = -1.25. In this case, Quantity A = 2, and Quantity B = 5
Here, Quantity B is greater than Quantity A

Answer: D
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 360 [0]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
The integers x and (x - 1) are not divisible by 4. [#permalink]
Exclude all multiples of 4 and their next successive numbers, i.e. include only 2,3 ... 6,7 ...10,11 ... 14,15 etc.
Let's focus on the required set of x containing 2,6,10,14, etc. We can see that every other number is added by 4, and we should only calculate a single case. This could be x=2 and 2/4=0.50

The tenths digit is always 5 and the hundredths digit is always 0

Answer is A
Carcass wrote:
The integers x and (x - 1) are not divisible by 4.

Quantity A
Quantity B
The value of the tenths digit of \(\frac{x}{4}\)
The value of the hundredths digit of \(\frac{x}{4}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 360 [2]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
The integers x and (x - 1) are not divisible by 4. [#permalink]
2
edited

Oh, I can see that negative values bring -1, -5, -9 as the x value possibilities and hence bifurcate answer choice A. Then it's D.

GreenlightTestPrep wrote:
Carcass wrote:
The integers x and (x - 1) are not divisible by 4.

Quantity A
Quantity B
The value of the tenths digit of \(\frac{x}{4}\)
The value of the hundredths digit of \(\frac{x}{4}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Sorry folks, but the correct answer is NOT A.
Since there's no information given that stipulates x must be positive, we must also consider negative values of x



The integers x and (x - 1) are not divisible by 4.
So, some possible values of x include: -6, -5, -2, -1, 2, 3, 6, 7, 10, 11, etc

Let's test a few values

If x = -6, we see that x/4 = -6/4 = -1.50. In this case, Quantity A = 5, and Quantity B = 0.
Here, Quantity A is greater than Quantity B

If x = -5, we see that x/4 = -5/4 = -1.25. In this case, Quantity A = 2, and Quantity B = 5
Here, Quantity B is greater than Quantity A

Answer: D

Originally posted by motion2020 on 31 Oct 2021, 13:51.
Last edited by motion2020 on 31 Oct 2021, 14:10, edited 1 time in total.
fixed by motion2020
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 155 [1]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
1
GreenlightTestPrep wrote:
Carcass wrote:
The integers x and (x - 1) are not divisible by 4.

Quantity A
Quantity B
The value of the tenths digit of \(\frac{x}{4}\)
The value of the hundredths digit of \(\frac{x}{4}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Sorry folks, but the correct answer is NOT A.
Since there's no information given that stipulates x must be positive, we must also consider negative values of x



The integers x and (x - 1) are not divisible by 4.
So, some possible values of x include: -6, -5, -2, -1, 2, 3, 6, 7, 10, 11, etc

Let's test a few values

If x = -6, we see that x/4 = -6/4 = -1.50. In this case, Quantity A = 5, and Quantity B = 0.
Here, Quantity A is greater than Quantity B

If x = -5, we see that x/4 = -5/4 = -1.25. In this case, Quantity A = 2, and Quantity B = 5
Here, Quantity B is greater than Quantity A

Answer: D
still answer is A, I think they forget to mention "positive integer."
Intern
Intern
Joined: 08 Aug 2022
Posts: 49
Own Kudos [?]: 33 [1]
Given Kudos: 98
Send PM
The integers x and (x - 1) are not divisible by 4. [#permalink]
1
When you divide an integer by 4, you know that your final value will have one of the following in decimal places: .00, 0.25, 0.50, or 0.75.

Just so you can trust me on this, let's check a few:
-4/4 = -1.00
-3/4 = -0.75
-2/4 = -0.50
-1/4 = -0.25
0/4 = 0.00
1/4 = 0.25
2/4 = 0.50
3/4 = 0.75
4/4 = 1.00
5/4 = 1.25
6/4 = 1.50
7/4 = 1.75
and so on...

Given that this pattern holds for all numbers, but then reverses when it goes positive to negative, let's just pick the simplest numbers we can from both positives and engatives. Looking at the start of our list above, what two numbers from 1-4 are next to each other and not divisible by 4? I see [1 & 2] or [2 & 3]. And then looking at the negatives, I see [-1 & -2] or [-2 & -3]

Option 1: x=2 and x-1 = 1
Option 2: x = 3 and x-1 = 2
Option 3: x = -1 and x-1 = -2
Option 4: x = -2 and x-1 = -3


So let's look at the remainders when these are divided by 4:
Option 1: 2/4 = 0.50 --> tenths place = 5, hundredths place = 0 --> the tenths place digit is greater (5 > 0)
Option 2: 3/4 = 0.75 --> tenths place = 7, hundredths place = 5 --> the tenths place digit is greater (7 > 5)
Option 3: -1/4 = -0.25 --> tenths place = 2, hundredths place = 5 --> ***the hundredths place digit is greater (5 > 2)***
Option 4: -2/4 = -0.50 --> tenths place = 5, hundredths place = 0 --> the tenths place digit is greater (5 > 0)

At first, when I only examined this problem using positive integers, I thought that quantity A was greater. However, when I realized integers can be negative, I realized that in option 3, the hundredths place is bigger, whereas in the other options, the tenths place is bigger. Thus, the answer is D - we cannot determine.
Manager
Manager
Joined: 11 Jun 2023
Posts: 77
Own Kudos [?]: 74 [0]
Given Kudos: 14
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
Carcass

I am curious about this question:
Consider the case of x=-1
You have -1*-2 -> not divisble by 4
but -1/4 is 0.25 which implies QB>QA

However if we take x=2 we have 2/4 -> 1/2 ->0.5 QA>QB

How can the OA be A if there are two conflicting cases?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29128
Own Kudos [?]: 34165 [0]
Given Kudos: 25525
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
Expert Reply
But in this case the logic is the reverse of my explanation here https://gre.myprepclub.com/forum/the-in ... tml#p10456

If you take negative numbers such as -1 and -2 the number you divide is -2 NOT -1

-1 is our x-1 and -2 our x. It is the reverse.

-1/4 is not our case

-2/4 it is
Manager
Manager
Joined: 11 Jun 2023
Posts: 77
Own Kudos [?]: 74 [0]
Given Kudos: 14
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
Carcass wrote:
But in this case the logic is the reverse of my explanation here https://gre.myprepclub.com/forum/the-in ... tml#p10456

If you take negative numbers such as -1 and -2 the number you divide is -2 NOT -1

-1 is our x-1 and -2 our x. It is the reverse.

-1/4 is not our case

-2/4 it is


Why would the number be -2? It says to divide x, and in our case x=-1, not x=-2. You can have x=-2 and x-1=-2-1=-3, which is also a valid case but so is x=-1.
User avatar
Intern
Intern
Joined: 09 Feb 2024
Posts: 7
Own Kudos [?]: 7 [1]
Given Kudos: 8
Send PM
Re: The integers x and (x - 1) are not divisible by 4. [#permalink]
1
Carcass
You are wrong if x=-1 x-1 is -2
so our case is -1/4
Verbal Expert
Joined: 18 Apr 2015
Posts: 29128
Own Kudos [?]: 34165 [0]
Given Kudos: 25525
Send PM
The integers x and (x - 1) are not divisible by 4. [#permalink]
Expert Reply
Thank you sir to point out this. appreciate

I said the other way around though
Prep Club for GRE Bot
The integers x and (x - 1) are not divisible by 4. [#permalink]
Moderators:
GRE Instructor
52 posts
GRE Forum Moderator
28 posts
Moderator
1092 posts
GRE Instructor
218 posts

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