Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1506:30 AM PDT
-07:30 AM PDT
Solve GRE practice problems covering Quant (One answer choice and multiple answer choice), Data Interpretation, Text Completion, Sentence Equivalence, and Reading Comprehension Problems.- Sep 15
07:30 AM PDT
-08:30 AM PDT
Solve 30 GMAT Focus practice problems covering Problem Solving, Data Sufficiency, Data Insights, Reading Comprehension, and Critical Reasoning. Take this GMAT practice quiz live with peers, analyze your GMAT study progress, and more. 
Sep 1201:30 PM IST
-11:30 PM IST
With brand new features like:AI-driven Planner tool, 850+ data Insights practice questions and GMAT Focus Edition Adaptive mock tests with ESR+ analysis and personal mentor support, our course is the most comprehensive course for GMAT Focus Edition.- Sep 16
08:30 AM PDT
-09:30 AM PDT
Are you stuck at a score and looking for effective score improvement strategies to achieve your target on GMAT? Meet Rajat, who improved his GMAT score by an incredible 70 points in just 12 days(and less than 50 hours of study) with GMATWhiz! - Sep 17
10:00 AM PDT
-11:00 AM PDT
In this video, Mayank Srivastava, Founder of Experts' Global, explains all the details about ISB PGP applications for 2024-25. 
Sep 2001:00 PM EDT
-02:00 PM EDT
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.- Sep 21
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test. 
Sep 2210:00 AM EDT
-11:00 AM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.
Each of the five divisions of a certain company sent representatives
[#permalink]
21 Sep 2019, 15:49
21 Sep 2019, 15:49
1
Kudos
97
Bookmarks
Show timer
00:00
A
B
C
D
E
Difficulty:
95%
(hard)
Question Stats:
45% (03:02) correct
55%
(02:52)
wrong
based on 1553
sessions
Each of the five divisions of a certain company sent representatives to a conference. If the numbers of representatives sent by four of the divisions were 3, 4, 5, and 5, was the range of the numbers of representatives sent by the five divisions greater than 2 ?
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
(2) The median of the numbers of representatives sent by the five divisions was 4.
DS06110.01
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
(2) The median of the numbers of representatives sent by the five divisions was 4.
DS06110.01
Senior Manager
Joined: 31 May 2018
Posts: 327
Given Kudos: 132
Location: United States
Concentration: Finance, Marketing
Each of the five divisions of a certain company sent representatives
[#permalink]
23 Sep 2019, 23:08
23 Sep 2019, 23:08
7
Kudos
10
Bookmarks
If the numbers of representatives sent by four of the divisions were 3, 4, 5, and 5 was the range of the numbers of representatives sent by the five divisions greater than 2?
STATEMENT (1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
let that 5th division send = 2 representatives
-- 2,3,4,5, and 5 (average = \(\frac{19}{5}\)=3.8 median = 4 and median>average)
range of the number of representatives = 5-2 = 3- was the range of the numbers of representatives sent by the five divisions greater than 2?--YES
let that 5th division send = 5 representatives
-- 3,4,5,5, and 5 (average = \(\frac{22}{5}\)=4.4 median = 5 and median>average)
range of the number of representatives = 5-3 = 2- was the range of the numbers of representatives sent by the five divisions greater than 2?--NO
we cant get the definite answer
INSUFFICIENT
STATEMENT (2) The median of the numbers of representatives sent by the five divisions was 4.
--median of five divisions = 4
--representatives sent by other divisions = 3,4,5, and 5
so the representatives sent by the fifth division --will be less than equal to 4
let 5th division sent = 4 representatives
--3,4,4,5, and 5
range = 5-3 = 2 -was the range of the numbers of representatives sent by the five divisions greater than 2?--NO
let 5th division sent = 2 representatives
--2,3,4,5, and 5
range = 5-2 = 3 -was the range of the numbers of representatives sent by the five divisions greater than 2?--YES
INSUFFICIENT
combining both statements together
median = 4 and median > average of the representatives
so, from here we know that 5th division sent less than equal to 4 represantatives
4 is not possible --3,4,4,5, and 5 (average = \(\frac{21}{5}\)=4.2 median = 4 and median<average)
3 is not possible --3,3,4,5, and 5 (average = \(\frac{20}{5}\)=4 median = 4 and median = average)
--1 and 2 are the possible number of representatives 5th division can send
in both cases median = 4 and median > average
range--1,3,4,5, and 5 = 5-1 =4
range--2,3,4,5, and 5 = 5-2 =3
was the range of the numbers of representatives sent by the five divisions greater than 2?--YES
SUFFICIENT
C is the answer
STATEMENT (1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
let that 5th division send = 2 representatives
-- 2,3,4,5, and 5 (average = \(\frac{19}{5}\)=3.8 median = 4 and median>average)
range of the number of representatives = 5-2 = 3- was the range of the numbers of representatives sent by the five divisions greater than 2?--YES
let that 5th division send = 5 representatives
-- 3,4,5,5, and 5 (average = \(\frac{22}{5}\)=4.4 median = 5 and median>average)
range of the number of representatives = 5-3 = 2- was the range of the numbers of representatives sent by the five divisions greater than 2?--NO
we cant get the definite answer
INSUFFICIENT
STATEMENT (2) The median of the numbers of representatives sent by the five divisions was 4.
--median of five divisions = 4
--representatives sent by other divisions = 3,4,5, and 5
so the representatives sent by the fifth division --will be less than equal to 4
let 5th division sent = 4 representatives
--3,4,4,5, and 5
range = 5-3 = 2 -was the range of the numbers of representatives sent by the five divisions greater than 2?--NO
let 5th division sent = 2 representatives
--2,3,4,5, and 5
range = 5-2 = 3 -was the range of the numbers of representatives sent by the five divisions greater than 2?--YES
INSUFFICIENT
combining both statements together
median = 4 and median > average of the representatives
so, from here we know that 5th division sent less than equal to 4 represantatives
4 is not possible --3,4,4,5, and 5 (average = \(\frac{21}{5}\)=4.2 median = 4 and median<average)
3 is not possible --3,3,4,5, and 5 (average = \(\frac{20}{5}\)=4 median = 4 and median = average)
--1 and 2 are the possible number of representatives 5th division can send
in both cases median = 4 and median > average
range--1,3,4,5, and 5 = 5-1 =4
range--2,3,4,5, and 5 = 5-2 =3
was the range of the numbers of representatives sent by the five divisions greater than 2?--YES
SUFFICIENT
C is the answer
Re: Each of the five divisions of a certain company sent representatives
[#permalink]
28 Sep 2019, 18:34
28 Sep 2019, 18:34
4
Kudos
1
Bookmarks
gmatt1476
Each of the five divisions of a certain company sent representatives to a conference. If the numbers of representatives sent by four of the divisions were 3, 4, 5, and 5, was the range of the numbers of representatives sent by the five divisions greater than 2 ?
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
(2) The median of the numbers of representatives sent by the five divisions was 4.
DS06110.01
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
(2) The median of the numbers of representatives sent by the five divisions was 4.
DS06110.01
Let integer x be the 5th number. The original question: Is R>2 ?
The range of the four known numbers is 5-3=2. The rephrased question: Is \(3\leq x\leq 5\) ?
1) We know that Me>A and can evaluate three possible cases.
Case 1: If \(x\leq 4\), then Me=4 and A=(17+x)/5.
4>(17+x)/5
x<3
The solution is x<3, which would give us a No answer to the rephrased question.
Case 2: If \(4<x\leq 5\), then Me=x.
x>(17+x)/5
4x>17
x>4.25
The solution is \(4.25<x\leq 5\), which would give us a Yes answer to the rephrased question.
Case 3: If x>5, then Me=5. We don't need to evaluate this case since we already have two different answers.
Thus, we can't get a definite answer to the rephrased question. \(\implies\) Insufficient
2) We know that Me=4, so \(x\leq 4\). If x is 4, then the answer to the rephrased question is Yes. However, if x is 1, then the answer to the rephrased question is No. Thus, we can't get a definite answer to the rephrased question. \(\implies\) Insufficient
1&2) Case 1 is the only valid case from statement 1). Thus, the answer to the rephrased question is a definite No. \(\implies\) Sufficient
Answer: C
