Test: Data Insights - 5 - GMAT MCQ

The equation being talked about is­ 
we want this expression in terms of only x and y. We have an extra in both numerator and denominator => 
So, divide numerator and denominator by a to get 

A given number is a possible value of [i]a’ if, for each value of x in the Table tab, there is a value of a that is compatible with that value of x and the other information provided. For each of the following numbers, select Yes if, given this condition, it is a possible value of a' Otherwise select No.[/i]
Now x has values 1/3, 1/4 etc, and xa has to be integer as xa is the number of contestants. Thus a has to be a multiple of LCM of denominators of values of x. Thus 12 or multiples of 12. 
Hence 9 and 10 are not valid while 12 is. 

a' = b' = xa = yb. 
Thus, a' = yb is true. 
a' = b' is also true. 
However, a + b < xa + yb is not true as xa < a and yb < b, resulting in a + b > xa + yb­

As can be seen, in both the blanks we are expected to fit in positive scenario or affirmative case.
So the options conveying negative meaning can be discarded. ‘Seldom, if ever, had’ and ‘tend not to have’ can be discarded.
Let us check the remaining options now.
A. tend to have: regularly behave/act in a particular way. So a general way that could be seen majority of time.
B. Almost always had: This is a very strong relationship. If I were to give a number I would say we talk of a thing happening at least 95% times.
C. Possibly had: The range of event happening could start as low as 10%. Maybe a slight chance.
Now the blanks that have to be replaced. 
Blank 1. Words should replace ‘strong positive correlation’. Now this would mean in most of the cases but is not extreme as shown by words ‘almost always had’. Only possibility - tend to have
Blank 2. Words should replace ‘more often than not’ and ‘strong negative correlation’. Again this would mean in most of the cases. Just tells us that the trend is in a particular way but not as extreme as the words ‘almost always had’. Only possibility - tend to have

Last Year Population was 200,500.
This Year Population is 2*(110,000) =220,000
Now this year total population = Last year population + (People Born this year) - (People who died last year)
220,000 = 200,500 + Y-X
Y - X = 19,500
Using options Y = 39,000 and X = 19,500­

Let's evaluate each statement by examining where each researcher stands on it. Remember, we are looking for one statement that Researcher X would disagree with and one that Researcher Y would disagree with.

The intermittency of renewable energy sources limits their effectiveness as a primary energy source.

• Researcher X acknowledges the issue by stating: "the intermittent nature of these energy sources—solar power being dependent on sunlight and wind power on wind conditions—means that significant investments must be made..."
• Researcher Y reinforces this point by saying: "Unlike wind and solar, nuclear power does not suffer from intermittency and can serve as a consistent base load energy source."
• Therefore, this statement cannot be the correct answer for either researcher.

Nuclear power is a crucial component in reducing global carbon emissions.

• Researcher X does not mention nuclear power, so we cannot determine whether he would agree or disagree.
• Researcher Y would agree with this statement. He says: "We must continue to invest in and improve existing nuclear power technologies, which provide a reliable and substantial amount of low-carbon energy."
• Therefore, this statement cannot be the correct answer for either researcher.

Significant investments in energy storage solutions can mitigate the challenges of renewable energy intermittency.

• Researcher X would agree with this statement. He says: "significant investments must be made in energy storage solutions and grid infrastructure to make renewable energy a reliable primary source."
• Researcher Y does not mention energy storage, so we cannot say he would disagree.
• Therefore, this statement cannot be the correct answer for either researcher.

Renewable energy technologies, even with supporting infrastructure, cannot be relied on as a primary energy source.

• Researcher X would disagree with this statement. He says: "The development of renewable energy technologies... should be our primary focus..." and adds that "significant investments must be made in energy storage solutions and grid infrastructure to make renewable energy a reliable primary source." This shows he believes renewables can be relied on as a primary energy source if properly supported, which directly contradicts the statement.
• Researcher Y would agree. He says that renewables are "not sufficient on their own to address the world's energy needs..." and adds that nuclear power "can reliably serve as a base load energy source." This suggests he supports nuclear, not renewables, as the primary dependable energy source.
• Therefore, this is the correct answer for Researcher X disagrees.

Wind and solar energy, without reliance on other sources, can serve as the core of a stable and scalable national energy supply.

• Researcher X says: "The development of renewable energy technologies... should be our primary focus..." and adds that supporting infrastructure is needed to make them reliable. He does not explicitly claim they can succeed without any other sources, so he may agree or remain neutral.
• Researcher Y would disagree with this statement. He says: "they are not sufficient on their own to meet global energy demands or meaningfully address climate change in the short term," and emphasizes that nuclear power "can serve as a consistent base load energy source." This shows he does not believe wind and solar, on their own, can form a stable and scalable supply — he views other sources, like nuclear, as essential.
• Therefore, this is the correct answer for Researcher Y disagrees.

Correct answer:
Researcher X "Renewable energy technologies, even with supporting infrastructure, cannot be relied on as a primary energy source."
Researcher Y "Wind and solar energy, without reliance on other sources, can serve as the core of a stable and scalable national energy supply."

Pipe A pumping in three times as much water as Pipe B implies that Pipe A pumped in 75% of the pool's capacity, while Pipe B pumped in the remaining 25% of the pool's capacity.

Assuming Pipe A takes x hours to fill the entire pool and Pipe B takes y hours to fill the entire pool, Pipe A would require 3x/4 hours to fill 75% of the pool, and Pipe B would require y/4 hours to fill the remaining 25% of the pool. Hence, we are given that 3x/4 + y/4 = 7, which simplifies to 3x + y = 28 and we need to find the value of y.

(1) After 4 hours, half of the pool was filled.
Given that initially Pipe A filled 75% of the pool, it must have also filled initial 50% of the pool by itself. Hence, this statement implies that Pipe A filled half of the pool in 4 hours. Thus, Pipe A would need 8 hours to fill the entire pool, making x equal to 8. Substituting x = 8 into 3x + y = 28 gives y = 4. Sufficient.

(2) Working together at their respective constant rates, Pipes A and B can fill the empty pool in one-third of the time it takes Pipe A, working alone at its constant rate.
­This implies that the combined rate of Pipe A and Pipe B is three times that of Pipe A alone. Thus, 1/x + 1/y = 3*1/x. Simplifying this gives x = 2y. Substituting x = 2y into 3x + y = 28 gives y = 4. Sufficient.

Answer: D.­

Let his first day's pay = x
His pay will be: Day 1 : x; Day 2: x + 11 ∗ 1; Day 3: x + 11 ∗ 2... Day 11: x + 11 ∗ 10
The total will come to: 
11x + 11 ∗ 55
If we can create an equation from a statement with which we can solve for the value of x, then the statement will be sufficient.­
(1) The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days.
First 4 days: x + (x + 1 ∗ 11) + (x + 2 ∗ 11) + (x + 3 ∗ 11)
Last 3 days: (x + 8 ∗ 11) + (x + 9 ∗ 11) + (x + 10 ∗ 11)
x + (x + 1 ∗ 11) + (x + 2 ∗ 11) + (x + 3 ∗ 11) = (x + 8 ∗ 11) + (x + 9 ∗ 11) + (x + 10 ∗ 11)
As there are more x x 's on one side than the other, one can isolate and solve for x. Thus this will be sufficient to solve the question.
Solving: x + (x + 1 ∗ 11) + (x + 2 ∗ 11) + (x + 3 ∗ 11) = (x + 8 ∗ 11) + (x + 9 ∗ 11) + (x + 10 ∗ 11)
x = 21 ∗ 11
x = 231
Which means that his total pay was: 11(231) + 11 ∗ 55 = 3416 

SUFFICIENT

(2) The total amount he was paid in the last 3 days of work equaled $66 more than the total amount he was paid in the first 3 days of work.
First 3 days: x + (x + 1 ∗ 11) + (x + 2 ∗ 11) 
Last 3 days: (x + 8 ∗ 11) + (x + 9 ∗ 11) + (x + 10 ∗ 11)
(x + 8 ∗ 11) + (x + 9 ∗ 11) + (x + 10 ∗ 11) = (6 ∗ 11) + x + (x + 1 ∗ 11) + (x + 2 ∗ 11) 
As there is an equal number of positive x x 's on either side of the equals sign, they will cancel one another out and leave no solution.

INSUFFICIENT

Answer: A

Group A: 7 kids, median age 13 (4th kid = 13).
Group B: 9 kids, median age 9 (5th kid = 9).
Exchange: Youngest (A1, B1) and oldest (A7, B9) swap.
New Group B: B2, B3, B4, B5, B6, B7, B8, A1, A7. Median is 5th age.
Statement (1): B9 = 12. Not enough, A1 and A7 unknown, median varies.
Statement (2): A1 = 8. Not enough, A7 and other B ages unknown, median varies.
Together: B9 = 12, A1 = 8. New ages: B2, B3, B4 < = 9, B5 = 9, B6, B7, B8 < = 12, 8, A7 > = 13. At least 4 ages (B2, B3, B4, 8) <= 9, so 5th is B5 = 9.
Conclusion: Both statements together give median 9.

Given - Brandon's compensation is structured so that each month he earns a $5000 base salary plus 10% of his total sales above $10000 for the month.
If we assume brandons sales figure as x for any month the equation we will able to form for total compensation is like below.
Total compensation = $5000 + 0.1 (x-$10000) -- (eq1)
lets find Brandon's total sales for the month of August using given conditions.

1st - Had Brandon sold $10000 more than he did in August, his total compensation for the month would have been equal to 15% of his sales.
Therefore equation will be form like, 
brandon new sales figure will be = x + $10000
$5000 + 0.1 (x + $10000 - $10000) = 0.15 ( x + $10000) 
5000 + 0.1x = 0.15x + 1500
3500 = 0.05x
x = 350000/5 = $70000.. Hence Sufficient.

2nd - Had Brandon sold $40000 less than he did in August, his total compensation for the month would have been equal to 10% of his sales.
Therefore equation will be form like, 
brandon new sales figure will be = x - $40000
$5000 + 0.1 (x - $40000 - $10000) = 0.1 (x - $40000)
if you see 0.1x will get cancelled on each side so there will be no solution.. Hence Not sufficient.
Answer A.

(1) This statement cites a study that found an association between social-media use by teenagers 10 to 15 years and an increase in the incidence of chronic anxiety or depression among 23% of the minors observed in the study. A key word here is association: It should be noted that this does not prove a cause-effect relationship, even if the study could motivate further investigation to see whether a causal mechanism could be identified. Even if a causal mechanism were identified, it could turn out that the use of social media was at least in part an effect of chronic anxiety or depression: Some teenagers might resort to social media use as a kind of escape mechanism. We should conclude that the information provided (even if the validity of the study is assumed) does not provide sufficient information to show definitively that the proposed restriction would result in developmental or health benefits for minors aged 10 to 15 years. The conclusion is that (1) is not sufficient alone; NOT sufficient.

(2) This statement indicates that use of social media by teens aged 10 to 15 years results in significant developmental benefits for 28% of teens in that age group. In other words, it indicates that social-media use by these teens causally contributes to a developmentally valuable effect. This implies that restriction of their social media use risks depriving a significant number of teens of the benefits resulting from their social-media use. So we can conclude that (2) is sufficient alone to provide a negative answer to the question posed; SUFFICIENT.

The correct answer is B; statement 2 alone is sufficient.

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?

3/4 are either roses or tulips, which implies R + T = 75.
3/25 are either lilies or tulips, which implies L + T = 12.
Observe that the above indicates that there must be some other kinds of flowers in the garden, for example, orchids.

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.
This implies that R/T < 13/2, which gives 2R < 13T.
Substituting R = 75 - T, we get:
2(75 - T) < 13T
150 - 2T < 13T
150 < 15T
T > 10
Since there is at least one lily, from L + T = 12 we get T = 11. This is sufficient.

(2) 13/20 of the flowers in the garden are either roses or lilies­.­
This implies that R + L = 65. Subtracting this from R + T = 75, we get T - L = 10. Adding this to L + T = 12, we get 2T = 22, which gives T = 11. This is sufficient too.
Answer: D.­

If we filter the question and remove all extraneous information, the question boils down to whether 
(1) P = 10,000
Substituting this value into the question, we'd get:

Since the answer to the above question is YES, then this statement is sufficient.
(2) n = 48­
Substituting this value into the question, we'd get:

 can be more than (or equal to) 50 as well as less than 50, depending on the value of P. Hence, this statement is not sufficient.

Let's simply analyze the speed increases between 5 and 10 meters:

• Hopping: ≈ 50% increase
• Speed walking: ≈ 10% increase
• Walking backward: ≈ 30% increase
• Walking forward: ≈ 10% increase

Now, let's evaluate the options:

• The average speed for hopping 3 meters would be greater than that for speed walking 3 meters.

The hopping speed for 5 meters is 2 meters per second, while the speed walking speed for 5 meters is 2.4 meters per second. Since the increase in hopping speed from 5 to 10 meters is greater than the increase in speed walking speed, it suggests that the hopping speed grows more rapidly over distance. Thus, the speed for hopping over 3 meters will decrease by a greater factor from 2 meters per second than the speed for speed walking will decrease from 2.4 meters per second. Answer - NO.

• The average speed for speed walking 15 meters would be greater than that for hopping 15 meters.

The speed for speed walking over 10 meters is 2.6 meters per second, while the speed for hopping over 10 meters is higher at 3.1 meters per second. Since hopping speed increases more rapidly with distance than speed walking, the speed for hopping over 15 meters will grow by a greater factor from 3.1 meters per second than the speed for speed walking will from 2.6 meters per second. Answer - NO.

• The average speed for walking backward 15 meters would be greater than that for walking forward 3 meters.

The speed for walking backward over 10 meters is 1.6 meters per second, while the speed for walking forward over 5 meters is also 1.6 meters per second. Both speeds increase over larger distances. Thus, the average speed for walking backward over 15 meters will increase from 1.6 meters per second, while the average speed for walking forward over 3 meters will decrease from 1.6 meters per second. 
Answer - YES.

Let a, b, and c be the numbers, respectively, of members in Groups P and M but not T, Groups P and T but not M, and Groups M and T but not P. The labeled diagram below shows for each of the 7 regions in the original diagram the number of stockholders in terms of a, b, and c. For example, since there are 12 members in Group M, it follows that the number of members in Group M only is 12 − (a + 8 + c) = 4 − a − c.­

We are to assume that each member of Group M belongs to Group P and determine the maximum possible number of members belonging to both Group T and Group P. From our assumption, it follows that 4 − a − c = 0 and c = 0, or a = 4 and c = 0. Using this information, and suppressing information about Group M (which is not relevant to answer the question), the labeled diagram above can be replaced with the labeled diagram below:

 

Because each of the three regions represents a nonnegative number of members, it follows that 237 − b ≥ 0, or b ≤ 237. Therefore, the number of members belonging to both Group T and Group P, namely 8 + b, is no more than 8 + 237 = 245. Moreover, letting a = 4, b = 237, and c = 0, it is easy to see from the first labeled diagram above that it is possible to have 245 members belonging to both Group T and Group P.

The correct answer is 245.

We are to assume that the number of members belonging to Group M and Group P is 10 and determine the maximum possible number of members belonging to both Group T and Group M. From our assumption, it follows that a + 8 = 10, or a = 2. Using this information, the first labeled diagram above can be replaced with the labeled diagram below:

 

Because 2 − c cannot be negative, it follows that c ≤ 2. Therefore, the number of members belonging to both Group T and Group M, namely 8 + c, is no more than 8 + 2 = 10. Moreover, letting a = 2, b = 0, and c = 2, it is easy to see from the first labeled diagram above that it is possible to have 10 members belonging to both Group T and Group M.

The correct answer is 10.

Median: It is the middle value of all the scores placed in an order. But here we are dealing with only % of scores in a given range, so we cannot find Median.
Mean: The above is true for mean too.
Range: The highest score vs the lowest score. Here, we do get know the higest and lowest for each day. So, Range is the only measure of tendency that can be found.

From the above , we can say that we will have Range for blank (A).

Range for all days will be the highest - lowest values for all 10 days = Highest of Day 2 - lowest of day 5 = 90 - 20 = 70.
The above gives us the answer for blank (B). when we combine day 2 and day 5, the range here too will become 70 as shown above.

The graph has three lines depicting number of employees and sales & cost. Further Profit = Sales - Cost
First Blank: We have to give the year tha had maximum profit per employee.
​
We don't require to calculate the value for each but scanning the graph should help us. 
As normal in the official questions, a seemingly easy question too has some trap/trick.
So, we look for the larger value of Sales- cost, which is nothing but the gap between orange line and blue line,  and smaller value for employees.
Scanning the graph, the lgaps are the biggest in year 2008, 2009 and 2011.
Now, 2008 is a trap because it is opposite of what we are seeking. The gap gives Cost - Sales, which is loss.
Let us see 2009 and 2011 now. The gap is almost same but the number of employees are much lesser in 2011.
So, the value of ​ will be largest for year 2011.

Second Blank: We have to give the year that had maximum percntage change in cost.
What one has to be careful on is the difference in maximum change vs maximum % change.
Although maximum change in cost is the drop of almost 112-8 or $104 billion, but drop will never be more than 100% here.
On the other hand, the increase in 2010 is 30 - 8 or $22 billion, a % increase of almost 300%. => 100*22/8
​
Answer: 2010

(A) Sum up all the points she scored. This is 396.
Calculate missed points in each sections (as said before, 42 and 36).
Percentages: Algebra 10.6%
Geometry 7.57%
Difference is ~3%, which is the correct answer

(B) From here its a simple percentage exercise:
% increase 4 to 5: (20 + 26 + 34)/(22 + 20 + 22) - 1 = 25%
% increase 2 to 3: (10 + 42 + 36)/(6 + 40 + 28) - 1 = ~18.9%
diff = 25 - 18.9 = 6.1%.

It must be the case that the median number of times per month respondents reported having communicated with patients by __(A)___ in the 2008 survey was less than that in the 2000 survey.
For which of telephone/email/video was the median for 2008 less than the median for 2000?
The median for telephone in 2000 is 2 or 3 or 4. Black region is where 50% is. 
The median for telephone in 2008 is 1. The 50% corresponds to the yellow region.
Hence the median is lower for telephone (Answer). For both email and video, median is the same in both years i.e. 0.

It must be the case that the percentage of respondents who reported having communicated with patients by both ___(B)___ was as great or greater in the 2008 survey as it was in the 2000 survey.
So we are looking for the overlap of two sets. We need this overlap to be higher or same in 2008 than in 2000. 
In 2008, 80% physicians communicated via telephone with their patients. (all regions except white)
In 2008, 40% physicians communicated via email with their patients. (all regions except white)
Hence there must be an overlap of at least 20% here. 20% physicians must have communicated via both. Think Sets.
In 2000, 83% physicians communicated via telephone with their patients. (all regions except white)
In 2008, 18% physicians communicated via email with their patients. (all regions except white)
Is it even possible that 20% communicated via both? No. At the most only 18% could have communicated via both. 
Hence answer is telephone and email. (Answer)

Let there be r red balls and total t balls.
The probability of drawing two red balls consecutively is 2/5.
Thus P = rC2/nC2 = 2/5 ...... r(r - 1)/n(n - 1) = 2/5 ......(i)
However, when 6 red balls are replaced with 6 white balls, the probability of drawing two consecutive red balls decreases to 3/20.

Red balls remaining = r - 6, while total remain n
Thus P = (r - 6)C2/nC2 = (r- 6)(r - 7)/n(n - 1) = 3/20......(ii)

Divide i by ii
r(r - 1)/(r - 6)(r - 7) = 40/15 = 8/3

Substitute the options to see what fits in for r.
r = 16
gives 16*15/10*9 or 8/3

Next substitute r in (i) to get n
16*15/n(n - 1) = 2/5
n(n -1) = 8*15*5 = 8*5*3*5 = 5*5*8*3 = 25*24
Hence total =25 and white = 25 - 16 = 9
After replacing Six red with white, white = 9 + 6 = 15