Last visit was: 23 Mar 2025, 00:52 It is currently 23 Mar 2025, 00:52
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
User avatar
gmatt1476
Joined: 04 Sep 2017
Last visit: 26 Nov 2024
Posts: 334
Own Kudos:
23,251
 [12]
Given Kudos: 61
Posts: 334
Kudos: 23,251
 [12]
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 21 Mar 2025
Posts: 1,855
Own Kudos:
Given Kudos: 707
Location: India
Posts: 1,855
Kudos: 7,453
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
MBABackstage
Joined: 13 Apr 2020
Last visit: 24 Jul 2020
Posts: 16
Own Kudos:
Given Kudos: 6
Location: United Kingdom
Posts: 16
Kudos: 66
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Kritisood
Joined: 21 Feb 2017
Last visit: 19 Jul 2023
Posts: 499
Own Kudos:
1,177
 [1]
Given Kudos: 1,091
Location: India
GMAT 1: 700 Q47 V39
Products:
GMAT 1: 700 Q47 V39
Posts: 499
Kudos: 1,177
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation \((a, b, c) Θ (d, e, f) = ad + be + cf\). What is the value of \((1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})\) ?

A. -1

B. 5/6

C. 1

D. 5/2

E. 3

PS37631.02

As per the given conditions: \((1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})\)

1*1=1 + (-2*-1/2=1) + (3*1/3=1) = 3 Ans E
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,771
Own Kudos:
33,117
 [1]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,771
Kudos: 33,117
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation \((a, b, c) Θ (d, e, f) = ad + be + cf\). What is the value of \((1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})\) ?

A. -1
B. 5/6
C. 1
D. 5/2
E. 3

PS37631.02

Given: (a, b, c) Θ (d, e, f) = ad + be + cf
So, (1,−2, 3) Θ (1, −1/2, 1/3) = (1)(1) + (-2)(-1/2) + (3)(1/3)
= 1 + 1 + 1
= 3

Answer: E

Cheers,
Brent
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 22 Mar 2025
Posts: 20,380
Own Kudos:
25,421
 [1]
Given Kudos: 292
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 20,380
Kudos: 25,421
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation \((a, b, c) Θ (d, e, f) = ad + be + cf\). What is the value of \((1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})\) ?

A. -1

B. 5/6

C. 1

D. 5/2

E. 3

PS37631.02

Plugging into the equation, we have:

1(1) + (-2)(-1/2) + 3(1/3) = 1 + 1 + 1 = 3

Answer: E
User avatar
perfectreview
Joined: 30 May 2020
Last visit: 07 Apr 2022
Posts: 18
Own Kudos:
Given Kudos: 1
Posts: 18
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given (a, b, c)Θ(d, e, f) = ad + be + cf and

\((1,−2,3)Θ(1,\frac{−1}{2},\frac{1}{3})\) = \((1 * 1) + (-2 * \frac{−1}{2}) + (3 * \frac{1}{3})\)

\((1,−2,3)Θ(1,\frac{−1}{2},\frac{1}{3})\) = 1 + 1 + 1 = 3

Option E
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 22 Mar 2025
Posts: 4,862
Own Kudos:
Given Kudos: 226
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,862
Kudos: 8,377
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SOLUTION:

(a,b,c)Θ(d ,e, f)=ad+ be +cf

In the expression (1,−2,3)Θ(1,−1/2,1/3) ,
a=1 d=1
b=-2 e=-1/2
c=3 f= 1/3


Using this operation, we have, ad+ be +c f

= (1.1) + (-2. -1/2) + (3.1/3)

= 1 + 1 +1

=3 (OPTION E)

Hope this helps :thumbsup:
Devmitra Sen(Math)
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 22 Mar 2025
Posts: 6,180
Own Kudos:
Given Kudos: 126
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,180
Kudos: 15,048
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation \((a, b, c) Θ (d, e, f) = ad + be + cf\). What is the value of \((1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})\) ?

A. -1

B. 5/6

C. 1

D. 5/2

E. 3

PS37631.02

Answer: Option E

Video solution by GMATinsight

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,669
Own Kudos:
Posts: 36,669
Kudos: 963
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:
Math Expert
100022 posts
PS Forum Moderator
503 posts