Last visit was: 01 Sep 2026, 08:35 It is currently 01 Sep 2026, 08:35
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
   1   2   3   4   
User avatar
Shin0099
User avatar
Joined: 26 Aug 2024
Last visit: 10 May 2026
Posts: 59
Own Kudos:
35
Given Kudos: 442
Posts: 59
Kudos: 35
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 13:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
That is a cool question!

So, what we can do here is the following: We can ignore the variables given completely and just assume, that these allow us to vary the signs in front of the numbers.
That said, we have as a max:
1+2+3+4+5 = 15
and as a min:
-1-2-3-4-5 = -15

As a result, we have a range of 30.

The result is E)
User avatar
Dereno
User avatar
Joined: 22 May 2020
Last visit: 30 Jul 2026
Posts: 1,399
Own Kudos:
1,414
 [1]
Given Kudos: 433
Posts: 1,399
Kudos: 1,414
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 13:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
The equation consists of 5 terms.

Term 1 outcome is positive if a>0 , and -ve if a <0

Term 2 = -2*b / (mod b) = -2 , when b>0 and 2 , when b<0 .

Term 3 = 3*(mod c)/ c = 3, when c >0 and -c when c<0 .

Term 4 = -4*d / (mod d) = -4, when d> 0 and 4, when d <0.

Term 5 = 5*(mod abcd) / (abcd) , = 5 when all +ve, or -5, when either odd terms are negative.

Case 1:

When a is positive , b is positive, c is negative and d is positive, hence abcd is negative .

Then the equation becomes 1-2-3-4-5 = -13

This is the maximum negative value that can be generated.

Case 2:

When a is positive, b is negative, c is positive and d is negative , and abcd is positive .

Then the equation becomes 1+2+3+4+5 = 15

This is the maximum value.

Range = 15-(-13) = 15+13 = 28.

Option D
User avatar
eshika23
User avatar
Joined: 01 Aug 2024
Last visit: 28 Jul 2026
Posts: 71
Own Kudos:
34
 [1]
Given Kudos: 65
Posts: 71
Kudos: 34
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 14:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To find the answer we need to first find highest and lowest value.

To make it lowest we need to keep max negative values.

Fraction will give one so assuming numbers wont affect we just have to concentrate on the negative and positive sign.

A for now lets assume it to be negative
B since a negative sign is present before it if b is -ve then the whole value will turn positive so B will be positive only.
C has a positive sign before so this will be negative.
D has a negative sign so this will be positive

Now we have
-a,+b,-c,+d when multiplied, this will give out +ve making 5 +ve. But we need it to be negative for lowest value.

and a is smallest so, we will make it positive.

Number will be:
+1-2-3-4-5=-13

To make it highest we will have to make each integer positive.

So, A=+ve, B=-ve, C=+ve, D=-ve (Product will also give positive)

Number will be:
+1+2+3+4+5=15

Range=highest-lowest
15-(-13)=15+13=28

Answer D
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
pappal
User avatar
Joined: 24 Nov 2022
Last visit: 11 Aug 2026
Posts: 383
Own Kudos:
129
Given Kudos: 120
Products:
GMAT Club Tests Forum Quiz
Posts: 383
Kudos: 129
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 15:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mod(a)/a-2b/mod(b)3*mod(c)/c-4mod(d)/dtotal
greater than 0+1-2+3-4-2
less than zero-1+2-3+4+2
according to the value of variable greater than or less than 0 above are the values of the first four terms which total up to the values
mentioned in the fifth column(total)
now we know that {5*mod(abcd)/abcd} can have only two values that are +5 and -5
to find out the range we must add up the extreme values
i.e. +5+2=7 and -5-2=-7
hence the range should be -7 to +7 a total of 15 values
User avatar
DylanD
User avatar
Joined: 08 Jan 2025
Last visit: 07 May 2026
Posts: 39
Own Kudos:
20
Given Kudos: 178
Location: United States
Posts: 39
Kudos: 20
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 15:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Topic(s)- Absolute Value, Max/Min, Range
Strategy- Max/Min
Variable(s)- Max Expression Value = "y"; Min Expression Value = "x"
Notation- absolute value = "abs"
Rephrase the Question: What is y - x?

1. Determine what each term could be
i. Note that the variables in each fraction will reduce to (+/- 1)/1
abs(a)/a-2*b/abs(b)3*abs(c)/c-4*d/abs(d)5*abs(a*b*c*d)/(a*b*c*d)
1/(1)-2*(1)/13*1/(1)-4*(1)/15*1/(1)
1/(-1)-2*(-1)/13*1/(-1)-4*(-1)/15*1/(-1)

2. Find the max and min value of the expression
i. Select the maximum value of each term
y = (1) + (2) + (3) + (4) + (5) = 15

ii. Select the minimum value of each term
x = (-1) + (-2) + (-3) + (-4) + (-5) = -15

3. Find the range of the expression
y - x = (15) - (-15) = 30

Answer: E
User avatar
MBAChaser123
User avatar
Joined: 19 Nov 2024
Last visit: 25 Dec 2025
Posts: 86
Own Kudos:
74
 [1]
Given Kudos: 7
Location: United States
Schools: Broad'26 (WL) Ross '26 (S)
GMAT Focus 1: 695 Q88 V83 DI82
GPA: 3
Schools: Broad'26 (WL) Ross '26 (S)
GMAT Focus 1: 695 Q88 V83 DI82
Posts: 86
Kudos: 74
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 17:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We know that the fraction \(\frac{|x|}{x} \) equals 1 if x is positive and equals -1 if x is negative.
So each expression equals the constant multiplied by either 1 or -1.
  • To find the highest limit of the total expression, we should see if it's possible for a,c, and abcd to be positive and b and d to be negative.
    If a,c are positive and b,d are negative, then abcd would be positive, and the result is: 1+2+3+4+5=15

  • To find the lowest limit of the total expression, we should see if it's possible for a,c, and abcd to be negative and b and d to be Positive.
    If a, c are negative and b,d are positive, then abcd will be positive. So, to still minimize the whole expression, we can assume that a is also positive, since it has the lowest constant multiplied by it. So, a,b,d are positive, and c,abcd are negative. And the result of the expression is: 1-2-3-4-5=-13

The question asks for the range of the expression, which is: 15-(-13)=28


Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
avatar
spvdrrooo
avatar
Joined: 20 Aug 2024
Last visit: 14 Aug 2026
Posts: 25
Own Kudos:
18
 [1]
Given Kudos: 139
Location: Belgium
Posts: 25
Kudos: 18
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 18:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For non-zero numbers a, b, c, and d, what is the range of values of the expression
|a| / a − 2b / |b| + 3|c| / c − 4d/|d| + 5|abcd| / abcd

First aknowledge that every fraction can be simplified

for every pos integer => |a| / a = 1
for every negative integer => |a| / a = -1

for every pos integer => 2b / |b| = 2
for every negative integer => 2b / |b| = -2

for every pos integer => 3|c| / c = 3
for every negative integer => 3|c| / c = -3

for every pos integer => 4d/|d| = 4
for every negative integer => 4d/|d| = -4

for every pos integer => 5|abcd| / abcd = 5
for every negative integer => 5|abcd| / abcd = -5

if we combine al the lowest possible values, lowest value would be = -1 + -2 + -3 + -4 + -5 = -15, but following the expression this would entail that we need to have an uneven amount of negative values so that the last term would be negative (-5) => therefore c would need to be negative and a,b and d would be positive.

=> resulting in 1 - 2 + (- 3) - 4 +(- 5) = -13 = lowest value for the expression

=> if b and d would be negative and a, c positive than the highest value for the expression will result in = 1 - (-2) + 3 - (-4) + 5 = 15

range = highest value - lowest value = 15 - (-13) = 28

answer D
User avatar
AVMachine
User avatar
Joined: 03 May 2024
Last visit: 26 Mar 2026
Posts: 190
Own Kudos:
156
 [1]
Given Kudos: 40
Posts: 190
Kudos: 156
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 18:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For non-zero numbers a, b, c, and d, what is the range (Max - Min) of values of the

expression: \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)


(a = +ve, b = -ve, c = +ve, d = -ve, then abcd = +ve)
Max: 1 + 2 + 3 + 4 + 5 = 15


(a = +ve, b = +ve, c = -ve, d = +ve, then abcd = -ve)
Min: 1 - 2 - 3 - 4 - 5 = -13;

Range: 15 - (-13) = 28;

A. 0
B. 13
C. 15
D. 28
E. 30
User avatar
Abhiswarup
User avatar
Joined: 07 Apr 2024
Last visit: 04 May 2026
Posts: 198
Own Kudos:
172
Given Kudos: 42
Location: India
Posts: 198
Kudos: 172
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 18:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In the expression abcd has been used
Now a can have 2 values +ve and -ve
Similarly b can have 2 values
c can have 2 values
d can have 2 values
Total combinations that can be made =2*2*2*2= 16
But options are 13 and 15 which are less tahn 16, options 0,28,30 are not possible
1st possible values
So some values will be repeating we have to check for all 16 values
a,b,c,d all are positive then abcd is also positive
Sum,S0=3

2nd possible values
one is negative three are positive
abcd becomes negative
Possible cases are 4C1
-abcd, a-bcd,ab-cd,abc-d
S1= -1-2+3-4-5= -9
S2=1+2+3-4-5=-3
S3=1-2-3-4-5=-13
S4=1-2+3+4-5=1
S1= -9, S2= -3, S3=-13,S4=1

3rd possible cases
2 are negative 2are positive
4C2= 6 possible cases and abcd is positive, substituting +ve and -ve
We get
S5=5, S6=-5,S7=9,S8=1, S9=15, S10=5

4th possible cases
Three are negative and one is positive
4C1 possible cases abcd is negative
S11=-11 ,S12=3 ,S13=-1 ,S15= -7

5th possible case
All are negative abcd is positive
S16= -1+2-3+4+5= 7
Total 16 values are there but S8,S4=1 have same value, S12, S0=3 has same values and S5, S10=5 has same values

So correct answer is 13 option B
User avatar
SRIVISHUDDHA22
User avatar
Joined: 08 Jan 2025
Last visit: 19 Aug 2026
Posts: 120
Own Kudos:
80
Given Kudos: 371
Location: India
Schools: ISB '26
GPA: 9
Products:
My Reviews
Schools: ISB '26
Posts: 120
Kudos: 80
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 20:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post


Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
Show Spoiler
Attachment:
GMAT-Club-Forum-wbq8kach.png
GMAT-Club-Forum-wbq8kach.png [ 103.95 KiB | Viewed 342 times ]
User avatar
SaKVSF16
User avatar
Joined: 31 May 2024
Last visit: 29 Aug 2026
Posts: 87
Own Kudos:
81
 [1]
Given Kudos: 41
Location: India
Schools: Sloan (MIT) Booth (Chicago) HBS Kellogg INSEAD
GMAT Focus 1: 695 Q87 V82 DI85
GPA: 3.7
Products:
My Reviews GMAT Club Tests
Schools: Sloan (MIT) Booth (Chicago) HBS Kellogg INSEAD
GMAT Focus 1: 695 Q87 V82 DI85
Posts: 87
Kudos: 81
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 21:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
the expression \( \frac{|a|}{a} = -1 \)if \(a < 0\), and \(+1\), if \(a>0 \)
similarly, \(\frac{b}{|b|} = -1\) if \(b<0\), and \(+1 \)if \(b>0 \)
We can see that each of the fractions in the expressions depend on the sign of the number involved, if number is negative, then that fraction will be -1, if number is positive, then that fraction will be +1

To find maximum number
We need to get as many fractions to be positive as possible
\(\\
a = +1, \frac{|a|}{a} = +1\\
b = -1, \frac{2b}{|b|} = -2\\
c = +1, \frac{3|c|}{c} = +3 \\
d = -1, \frac{4d}{|d|} = -4 \\
abcd = +1, \frac{5|abcd|}{abcd} = +5 \\
\)

Sum = +1 -(-2) + 3 -(-4) +5 = 1+2+3+4+5 = 15, this is the max we can get because all components are positive here
Max = 15

To find minimum number, we need to get as many components to be negative as possible,
trying to get all components negative not possible because>>
\(a = -1, \frac{|a|}{a} = -1\\
b = +1, \frac{2b}{|b|} = +2\\
c = -1, \frac{3|c|}{c} = -3 \\
d = +1, \frac{4d}{|d|} = +4 \\
abcd = +1, \frac{5|abcd|}{abcd} = +5 \\
\\
\)

then sum= -1-2-3-4+5 = 5-10 = -5

To get minimum, we can afford having a to be positive, so that we can get abcd = -1,
\(a = +1, \frac{|a|}{a} = +1\\
b = +1, \frac{2b}{|b|} = +2\\
c = -1, \frac{3|c|}{c} = -3 \\
d = +1, \frac{4d}{|d|} = +4 \\
abcd = -1, \frac{5|abcd|}{abcd} = -5\)

then sum = +1-2-3-4-5 = 1-14= -13


Range = 15-(-13) = 15+13 = 28
Answer is D
User avatar
Tanish9102
User avatar
Joined: 30 Jun 2025
Last visit: 20 Nov 2025
Posts: 59
Own Kudos:
49
Posts: 59
Kudos: 49
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 21:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Correct Answer: Option E 30

Here we will find out minimum and maximum values to find out range:

1) Let's find out maximum values first,
Here we keep,
a= 1
b= 2
c= 3
d= 4

|a|/a - 2b/|b| + 3|c|/c - 4d/|d| + 5|abcd|/abcd
|1|/1 - 2*2/|2| + 3*|3|/3 - 4*4/|4| + 5*|1*2*3*4|/1*2*3*4
1+2+3+4+5= 15

2) Now find out minimum values,
Here we keep,
a= -1
b= -2
c= -3
d= -4

|a|/a - 2b/|b| + 3|c|/c - 4d/|d| + 5|abcd|/abcd
|-1|/-1 - 2*-2/|-2| + 3*|-3|/-3 - 4*-4/|-4| + 5*|-1*-2*-3*-4|/-1*-2*-3*-4
-1-2-3-4-5= -15
Now if we need to find range= Maximum-Minimum
= 15- (-15)
= 30
User avatar
Prathu1221
User avatar
Joined: 19 Jun 2025
Last visit: 20 Jul 2025
Posts: 62
Own Kudos:
40
Given Kudos: 1
Posts: 62
Kudos: 40
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 22:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To maximise we need to ensure that all values are of same sign otherwise they will decrease the final value.
Now the absolute value of coefficients is 1+2+3+4+5=15
Let us try to make minium value as zero because if we make any value negative it will have an effect on the 15 we calculated earlier.
If signs are a,b,c,d=pos,neg,pos,neg it will eventually come as zero.
So range of values is 15.
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
Manu1995
User avatar
Joined: 30 Aug 2021
Last visit: 11 Jul 2026
Posts: 81
Own Kudos:
55
 [1]
Given Kudos: 18
Posts: 81
Kudos: 55
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 22:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For any non-zero number x, the term \(\frac{|x|}{x}\) has only two possible values:

If x > 0, then \(\frac{|x|}{x}\) = \(\frac{x}{x}\) = 1.
If x < 0, then \(\frac{|x|}{x}\) = \(\frac{-x}{x}\) = -1

From given expressions:

==>\(\frac{|a|}{a}\): The value is either 1 (if a>0) or -1 (if a<0).
==> \(-\frac{2b}{|b|}\): The value is either -2(1) = -2(b>0) or -2(-1)=2(b<0).
==>\(\frac{3|c|}{c}\): The value is either 3(1) = 3(if c>0) or 3(-1)=-3(if c<0)
==>\(-\frac{4d}{|d|}\):The value is either -4(1) = -4(d>0) or -4(-1)=4(d<0)
==>\(\frac{5|abcd|}{abcd}\): This term depends on the sign of the product abcd. If abcd > 0, the value is 5(1) = 5. If abcd < 0, the value is 5(-1) = -5

Now finding the maximum value:
To find the max values we need each term to be positive:
From the above expressions the max possible value is = 1(a>0)+2(b<0)+3(c>0)+4(d<0)+5(abcd>0)= 15
and product of the signs is also positive which means abcd>0

Now finding the minimum value:
To minimize the expression, assign signs to make each term as small as possible, ensuring consistency with abcd(abcd<0):
From the previous analysis, the minimum occurs when(a>0),(b>0),(c<0),(d>0):
Now from above expressions:
\(\frac{|a|}{a}\)= 1 ,\(-\frac{2b}{|b|}\)= -2,\(\frac{3|c|}{c}\)= -3, \(-\frac{4d}{|d|}\)= -4
Sum of first 4 terms = 1-2-3-4= -8
Product abcd < 0 (c<0), so
\(\frac{5|abcd|}{abcd}\) = -5
Total = -8-5 = -13

Range= Max value -Min value
= 15-(-13)= 28

Final answer Option D
User avatar
tgsankar10
User avatar
Joined: 27 Mar 2024
Last visit: 31 Aug 2026
Posts: 281
Own Kudos:
407
 [1]
Given Kudos: 85
Location: India
Posts: 281
Kudos: 407
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 23:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
When all of \(a,b,c,d\) are positive the expression will result in \(1-2+3-4+5=3\)

When all of \(a,b,c,d\) are negative the expression will result in \(-1+2-3+4+5=7\)

The maximum value of expression will occur when all the terms in expression is positive. When \(b & d\) are negative, the value is \(1+2+3+4+5=15\)

To minimize the value, all the terms of expression must be negative. For that \(\text{a & c}\) must be negative. If that's the case the 5th term of expression will be positive.

When only \(c\) is negative, the value of expression is \(1-2-3-4-5=-13\)

Range of values \(=15-(-13)=28\)

Answer: D
User avatar
chasing725
User avatar
Joined: 22 Jun 2025
Last visit: 16 Aug 2026
Posts: 241
Own Kudos:
235
 [1]
Given Kudos: 6
Location: United States (OR)
Schools: Stanford
Schools: Stanford
Posts: 241
Kudos: 235
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 23:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more

Range = Maximum - Minimum

For Maximum value each term should be positive. For that to happen,

a should be positive
b should be negative
c should be positive
d should be negative

abcd should be positive

Max Value = 1 + 2 + 3 + 4 + 5 = 15

For minimum value we should try to have maximum negative value as abcd should be negative.

In that case, we can have

d positive
c negative
b positive
a positive

Minimum value = -5 - 4 - 3 -2 +1 = -13

Range = 15 + 13 = 28

Option D
User avatar
HarshaBujji
User avatar
Joined: 29 Jun 2020
Last visit: 29 Aug 2026
Posts: 725
Own Kudos:
939
 [1]
Given Kudos: 247
Location: India
Products:
My Reviews
Posts: 725
Kudos: 939
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 23:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
We know that |a| = -a if a<0,
= a if a>=0.

Using this principle, let's find the max and min values of this equation so that we can find the range.

Max values:
Let a>0, b<0, c>0, d<0 , In this case abcd>0. Now let's simplify the equation using above above-stated principle.

\(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\) = 1+2+3+4+5 = 15.

The maximum value of this expression is 15.

Min values:
Let a>0, b>0,c<0,d>0, So abcd<0. Now let's simplify the equation using above above-stated principle.
\(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\) = 1-2-3-4-5 = -13.

The minimum value of the expression is -13.

Hence range is 28. IMO D
User avatar
Pavan98
User avatar
Joined: 12 Jun 2025
Last visit: 27 Mar 2026
Posts: 13
Own Kudos:
10
 [1]
Given Kudos: 1
Posts: 13
Kudos: 10
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 11 Jul 2025, 23:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Range is max. value - min. value
Finding max value, we need to make all the negative signs become positive
hence a = a, b= -b, c= c, d=-d
max value = 1 - (-2) + 3 - (-4) + 5 = 15

Finding min value, we need to make all positive signs negative
i.e a=-a, b=b, c=-c, d=d
Hovewer with this abcd will become positive and increase it by +5
Hence we need to make a=-a as +1 will make lesser difference than +5
so a=a, b=b, c=-c, d=d
min value = 1 - 2 + (-3) - 4 + (-5) = -13

Hence range = 15 - (-13) = 28
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
sanjitscorps18
User avatar
Joined: 26 Jan 2019
Last visit: 03 Mar 2026
Posts: 723
Own Kudos:
757
 [1]
Given Kudos: 130
Location: India
Schools: IMD'26
Products:
My Reviews
Schools: IMD'26
Posts: 723
Kudos: 757
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 12 Jul 2025, 00:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For non-zero numbers a, b, c, and d, what is the range of values of the expression \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

A. 0
B. 13
C. 15
D. 28
E. 30


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more

\(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\)?

Let's say
a = +ve,
b = -ve,
c = +ve,
d = -ve,
abcd = +ve

=> \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\) = 1+2+3+4+5 = 15

For range we have to find the lowest possible number
Let's say
a = +ve,
b = +ve,
c = -ve,
d = +ve,
abcd = -ve

=> \(\frac{|a|}{a} - \frac{2b}{|b|} + \frac{3|c|}{c} - \frac{4d}{|d|} + \frac{5|abcd|}{abcd}\) = 1-2-3-4-5 = -13

Range = 15 - (-13) = 28

Option D
User avatar
asingh22
User avatar
Joined: 31 Jul 2024
Last visit: 31 Mar 2026
Posts: 68
Own Kudos:
57
 [1]
Given Kudos: 8
Location: India
Schools: Foster '26 (II) Goizueta '26 (S) Scheller '26 Anderson '26 Darden '26 Kelley '26 Kellogg '26 Ross '26 Sloan '26 UNC '26 (S) Stern '26 Yale '26 Haas '26 Owen '26 (II)
GMAT Focus 1: 635 Q84 V78 DI82
GMAT Focus 2: 655 Q89 V80 DI78
GPA: 2.5
Schools: Foster '26 (II) Goizueta '26 (S) Scheller '26 Anderson '26 Darden '26 Kelley '26 Kellogg '26 Ross '26 Sloan '26 UNC '26 (S) Stern '26 Yale '26 Haas '26 Owen '26 (II)
GMAT Focus 2: 655 Q89 V80 DI78
Posts: 68
Kudos: 57
 [1]
GMAT Club Olympics 2025 (Day 10): For non-zero numbers a, b, c, and d 12 Jul 2025, 01:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
to maximize, convert all the values into +

for a, it's already positive, then a +, b has - in front of it, to make it positve, b should be negative, like this for c and d
a +, b -, c + and d - , abcd = +

1+2+3+4+5 = 15 Max

For minimum let's make lowest negative number; for this change all signs into negative
a = -, b +, c - and d + , and abcd +

-1-2-3-4+5 = -5

But wait, the highest number abcd is positive, we need to change it to negative, then let's inverse 1 number, we will pick the lowest number to minimize the negative number
a + , then abcd = -

1-2-3-4-5 = - 13.

Range then 15-(-13) = 28
   1   2   3   4   
Moderator:
Bunuel
Math Expert
113010 posts