List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The in...

Join the Discussion on the App

List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?

1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.

2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'A'. Can you explain this answer?

Join for Free

Join for Free

Verified Answer

List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are us...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

List A:{1,2,3…9,10}, a total of 10 integers
Let the total number of integers in set P be x
- Let the integers used once from list A = a
- Let the integers used twice from list A = b
Let the total number of integers in set Q be y
- Let the integers used once from list A = c
- Let the integers used twice from list A = d

To Find: Number of integers used more than once

Number of integers used more than once = Number of integers used two times
So number of integers used two times = Total number of integers in set P and set Q – number of integers used one time
- So, b+d = (x+y) – (a+b)
- Since all integers are used atleast once,
  - so a+b =10
- So, b+d = (x+y)-10

So to determine the number of integers used more than once, we will have to find value of (x+y).

Step 3: Analyze Statement 1 independently

The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.

So, Total Integers in set P = x = 10 – 2 = 8
So, Total Integers in set Q = y = 10 – 3 = 7
x + y = 15

Since we know the value of x+y, we will find the answer.

Sufficient to answer.

Step 4: Analyze Statement 2 independently

The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.

Sum of integers in list A = 1+2+3….+10 = S, say

Sum of integers in sets P and Q = 1+2+3…+10 + Sum of repeated integers

Difference in sum of the integers in sets P and Q = S + sum of repeated integers – S = Sum of repeated integers

Sum of Repeated integers = 15

So, the sum of repeated integers 15 can be expressed as a sum of integers in various ways.
- For ex: (9, 6) gives the sum as 15 and number of repeated integers =2
- or (4, 5, 6) gives the sum as 15 and number of repeated integers = 3

Since we do not know the exct number of repeated integers, we will not be able to determine the value of x &y

Insufficient to answer

Step 5: Analyze Both Statements Together (if needed)

As we have a unique answer from step-3, this step is not required.

Answer: A

This question is part of UPSC exam. View all GMAT courses

View all answers Start learning for free

Explore Courses for GMAT exam

Similar GMAT Doubts

Two shopkeepers, Bruce and Wayne, sold the same toy at different prices. If the ratio of the prices at which Bruce and Wayne purchased the toy was 3:4 respectively, who made a greater profit on selling the toy?(1) The profit percentage of Bruce was higher than that of Wayne.(2) The ratio of the prices at which Bruce and Wayne sold the toy was 4:3 respectively.

View answer

Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.How many integers are there between m and n, exclusive, if m and n are themselves integers?(1) m − n = 8(2) There are 5 integers between, but not including, m − 1 and n − 1.

View answer

Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.A certain number is not an integer. Is the number less than .4?(1) The number rounded to the nearest tenth is .4.(2) The number rounded to the nearest integer is 0.

View answer

What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.

View answer

From a group of 6 employees, k employees are chosen to be on the party-planning committee. If k is a positive integer, what is the value of k?(1) k is a prime number(2) There are 15 different ways to create the party-planning committee consisting of k employees.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?.

Solutions for List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam