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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6 (B) 16 (C) 22 (D) 30 (E) 174

Problem Solving Question: 18 Category:Arithmetic Properties of numbers Page: 64 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
02 Jan 2014, 05:34

Expert's post

SOLUTION

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6 (B) 16 (C) 22 (D) 30 (E) 174

The number of integers that belong to set X ONLY is 10-6=4; The number of integers that belong to set Y ONLY is 18-6=12;

The number of integers that belong to set X or set Y, but not both is 4+12=16.

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6 (B) 16 (C) 22 (D) 30 (E) 174

As per Set theory : A@B= A + B - 2(A n B), so 10 + 18-2*6 = 16 _________________

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
02 Jan 2014, 23:53

1

This post received KUDOS

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6 (B) 16 (C) 22 (D) 30 (E) 174

Attachment:

untitled1.PNG [ 3.39 KiB | Viewed 1555 times ]

Sol: Look at above figure. Now X@Y = Number of elements in X and Y which are not present in Both.

So X@Y= 10-6+18-6= 16 Ans B _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
03 Jan 2014, 03:03

1

This post received KUDOS

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6 (B) 16 (C) 22 (D) 30 (E) 174

Exactly 1 = X + Y - 2(X&Y)

When you add X and Y the intersection gets added twice hence we have to deduct it twice

Exactly 1 = 10 + 18 - 12 = 16

Answer B _________________

Perfect Scores

If you think our post was valuable then please encourage us with Kudos

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
05 Jan 2014, 10:13

Expert's post

SOLUTION

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6 (B) 16 (C) 22 (D) 30 (E) 174

The number of integers that belong to set X ONLY is 10-6=4; The number of integers that belong to set Y ONLY is 18-6=12;

The number of integers that belong to set X or set Y, but not both is 4+12=16.