by: Alae17
54 mins
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 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
GMAT 1: 660 Q43 V47
Posts: 31
Updated on: 24 Jan 2024, 00:26
Originally posted by tickledpink001 on 31 Dec 2023, 01:49.
Last edited by Bunuel on 24 Jan 2024, 00:26, edited 3 times in total.
Last edited by Bunuel on 24 Jan 2024, 00:26, edited 3 times in total.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:06) correct
36%
(02:10)
wrong
based on 1153
sessions
History
Date
Time
Result
Not Attempted Yet
Was the median height of the 25 children in a certain class at least 2 percent greater than the average (arithmetic mean) height of the 25 children?
(1) The median height of the 25 children was 2 centimeters greater than their average height.
(2) The sum of the heights of the 25 children was less than 2,550 centimeters
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
focus.png [ 45.31 KiB | Viewed 14607 times ]
(1) The median height of the 25 children was 2 centimeters greater than their average height.
(2) The sum of the heights of the 25 children was less than 2,550 centimeters
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
Attachment:
focus.png [ 45.31 KiB | Viewed 14607 times ]
Pro tip:
Combine official questions for familiarity with GMAT Club Tests for analytics and tougher Focus-level practice so the real exam feels manageable.
Explore →
Was the median height of the 25 children in a certain class at least 2 percent greater than the average (arithmetic mean) height of the 25 children?
Is median height\(\geq \) 102 % of Average height.
(1) The median height of the 25 children was 2 centimeters greater than their average height.
Median height =Average height+2
If Average height is 100cm or less, 2cm will be at least 2% of the average height. Answer is YES
If Average height >100cm, answer is NO.
Insufficient
(2) The sum of the heights of the 25 children was less than 2,550 centimeters
So Average \(\leq \frac{2550}{25}\) or 102cm.
Nothing about Median height.
Insufficient
Combined
If average height is 100 or less, answer is yes.
If Average height is between 100 and 102, answer is No.
insufficient
E
_________________
Is median height\(\geq \) 102 % of Average height.
(1) The median height of the 25 children was 2 centimeters greater than their average height.
Median height =Average height+2
If Average height is 100cm or less, 2cm will be at least 2% of the average height. Answer is YES
If Average height >100cm, answer is NO.
Insufficient
(2) The sum of the heights of the 25 children was less than 2,550 centimeters
So Average \(\leq \frac{2550}{25}\) or 102cm.
Nothing about Median height.
Insufficient
Combined
If average height is 100 or less, answer is yes.
If Average height is between 100 and 102, answer is No.
insufficient
E
_________________
tickledpink001
Given the heights of 25 children, is median of heights at least 2% more than mean of heights?
(1) The median height of the 25 children was 2 centimeters greater than their average height.
Median = Mean + 2 cm
This tells us the absolute difference between the two, not the percentage difference.
e.g.
If mean = 50 cm, then median = 52 cm and it is 4% more than mean.
If mean = 100 cm, then median = 102 cm and it is exactly 2% more than mean.
But if mean = 200 cm, then median = 202 and it is merely 1% extra.
Not sufficient alone.
(2) The sum of the heights of the 25 children was less than 2,550 centimeters
Obviously not sufficient alone.
Using both together,
Sum of heights < 2550 i.e. mean < 102 cm
When mean = 100, median = 102 and this is when median is exactly 2% more than mean.
When mean < 100, median will be more than 2% extra and when mean > 100, median will be less than 2% extra.
Since we are given that mean < 102, it could be less than 100 or more than 100. Hence median could be more than 2% extra or less than 2% extra. Not sufficient.
Answer (E)
_________________
-
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
General Discussion
Silly mistake - missed "less than" in (2), which led me to select C instead of E
Posts: 2
chetan2u
I want to know what I am doing incorrectly in my approach:
question is asking if the median is at least 2% greater than the average, which in equation is:
(median/average) - 1 >= 0.02
(1) states median is 2 cm greater than the average height, hence median = average + 2
substituting this into the equation above, i get: (average + 2)/(average) - 1 >= 0.02
simplify:
(average)/(average) + (2)/(average) - 1 >= 0.02
1 + (2/average) - 1 >= 0.02
2/average >= 0.02
2/0.02 >= average
average <= 100
given average is less than or equal to 100, at its max value:
average = 100, median = 102 -> median is at least 2% greater than average
if average is any value below 100, median is larger by more than 2%:
i.e. if average = 50, median = 52
52/50 -1 = 0.04 or 4%
by this logic, wouldn't (1) be sufficient to answer the question?
nishantc1999
From (1) we do not get that \(0 < average \leq 100\). When you substitute median = average + 2 into the question "is \(\frac{median}{average} - 1 \geq 0.02\)?", the question becomes "is \(0 < average \leq 100\)?"
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Posts: 2
Bunuel
Thanks so much for the response! If I understand correctly, the mistake I made was assuming the median/average - 1 >= 0.02 to be true when really it is the initial question that is asked. and if you simplify that with median = average + 2, then the question simply changes to average <= 100, and it doesn't confirm that the average is in fact <= 100.
thanks so much!
nishantc1999
The initial question was "is \(\frac{median}{average} - 1 \geq 0.02\)?". Then, after substituting, median = average + 2 into the question, you just rephrased the question into "is \(0 < average \leq 100\)?"
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
was median > (102/100)* avg ?
1) median = 2cm + Avg --- we can find some giants that are really really big and force this difference to be less than 2%., and force this to show a much greater difference that exceeds a 2% ratio, by selecting some really really short people.
2) this constraint narrows down the giants, and really short people so...
ill take 2 edge cases:
avg = 2550/25 = 102
avg = 25/25 = 1 , no info on median, so i cant say for sure.
1),2) -> median = 2+ 102 ----> 104/102 = 1.01960784314 ... so thats 1.9 percent (so no)
median = 2+ 1 ----> 3/1 = 3 ... thats 200% greater (so yes)
E.
1) median = 2cm + Avg --- we can find some giants that are really really big and force this difference to be less than 2%., and force this to show a much greater difference that exceeds a 2% ratio, by selecting some really really short people.
2) this constraint narrows down the giants, and really short people so...
ill take 2 edge cases:
avg = 2550/25 = 102
avg = 25/25 = 1 , no info on median, so i cant say for sure.
1),2) -> median = 2+ 102 ----> 104/102 = 1.01960784314 ... so thats 1.9 percent (so no)
median = 2+ 1 ----> 3/1 = 3 ... thats 200% greater (so yes)
E.
Moderators:
Announcements
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.