For each of three years and five survey prompts, the table shows the

Question

For each of three years and five survey prompts, the table shows the percentage of respondents to a job-satisfaction survey who agreed with the prompt. For columns showing pairs of years in the top row, a minus sign (–) or plus sign (+) for a prompt indicates that the change in the percentage of respondents from the first year to the second represents a significant decrease or significant increase, respectively. For the difference in the number of percentage points to be considered significant, its absolute value must be greater than a certain number, x. Although the percentages in the table are rounded to the nearest percentage point, whether a change is significant is determined using the raw percentages prior to rounding.

For each of the following values, select Could be x if that exact value for x is consistent with the information provided. Otherwise, select Cannot be x.

Prompt  
  2013  
  2014  
  2015  
  2013 to 2014  
  2014 to 2015  
 
  (1) I understand my organization. 
 63% 
 59% 
 61% 
 - 
 + 
 
  (2) I understand my role in the organization 
 72% 
 69 
 70% 
 - 
 . 
 
  (3) I am empowered to innovate. 
 58% 
 55% 
 57% 
 - 
 + 
 
  (4) My work is gratifying. 
 72% 
 70% 
 70% 
 - 
 . 
 
  (5) I am good at my job. 
 84% 
 82% 
 83% 
 - 
 +

For each of the following values, select  Could be x  if that exact value for  x  is consistent with the information provided. Otherwise, select  Cannot be x .

KarishmaB · Accepted Answer

Essentially, the question is testing you on your rounding basics. Diff in percentage points from one year to another was calculated. If it was more than x, a +/- was put. If it was less than x, it was left blank.
Then the given values in the table were rounded. So each given value, say 63% could actually be anything from 62.5% (including) to 63.5%(excluding).

Focus on the values where the difference is smallest possible but 'significant'.
In 14-15, 82% - 83% is significant. Here the actual difference could be 81.5% to a little less than 83.5%. So the maximum actual difference could be slightly less than 2. So x can be slightly less than 2 but it cannot be 2. If x were 2, then this would have been 'not significant.'

Focus on the values where the difference is largest possible but 'not significant'.
In 14-15, 69% - 70% is not significant
These could be a little less than 69.5% and 69.5% so the minimum value of x could be very little (slightly more than 0).
Say actual values here could be 69.4% - 69.5%. Then if x = 0.1, even then these would be 'not significant'.

Hence x can easily take very small values so 0.9 and 1.4 are both acceptable.

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Attachment:

GMAT-Club-Forum-ds19se3d.png

chetan2u · Answer

For the difference in the number of percentage points to be considered significant, its absolute value must be greater than a certain number, x.

What are the different differences given: 1%, 2% and 3%.
But we are looking at the least possible value, x, so that value should satisfy the difference of 1%.

One such difference given is 69 to 70.
69 could be 68.5 to 68.499999 when not rounded. Similarly 70 would be 69.5 to 70.499999.

The maximum difference, therefore will be 70.499999 - 68.5 = 1.99999999

0.9 could fit in with 69 and 69.9(rounded to 70)
1.4 could fit in with 69 and 70.4(rounded to 70)
However, 2 will not fit in as then 1% taken as significant will not be permitted

Iwillget770 · Answer

Hi KarishmaB , Lets Focus on the year 14-15 for Point no 3. Here values can be 54.5 ( inclusive ) and 57.5 (exclusive) So the values can be anything between 0 and 3. So all the options are possible. Please guide. Regards GMAT-Club-Forum-whyfw7fg.png

KarishmaB · Answer

A possible value of x should work for the entire table. If there is even one reading for which it doesn't work, then that value is not possible. x = 3 does not work for 82% - 83% being significant. If x = 3, this CANNOT be significant and the table becomes false. This is not acceptable. GMAT-Club-Forum-5fa5uztc.png

Aabhash777 · Answer

The max value for rounding is +0.4999, while the least is 0.

Difference  Min    Max 
                70     70.49 
 Min 69        1       1.49 
 Max 69.49    0.51    1

The answer could range from 0.51 to 1.49. Here 2 is the only option that does not fit

Araevin · Answer

x is an absolute value used as a threshold to decide whether an absolute difference in percentages is significant or insignificant, which means
1) We’re trying to find the min value of x, beyond which the difference is significant
2) This also means we’re trying to find the max value of x, below which the difference is insignificant

For the first part, look for values where difference of rounded off values is min but was still considered significant.
This is row 5, column 2014-2015 where values are a = 83 & b = 84, this implies actual values of
82.5 =< a < 83.5
83.5 =< b < 84.5
To get the min of x, subtract max a from min b (since we’re dealing with absolute values, we’re subtracting smaller numbers from bigger numbers throughout)
To get the max of x, subtract min a from max b
Therefore 0 < x < 2 ( important to note, x is not 0 and not 2)

For the second part, look for values where difference of rounded off values is max but was still considered insignificant.
This is row 2, column 2014-2015 where values are c = 69 & d = 70, this implies actual values of
68.5 =< c < 69.5
69.5 =< d < 70.5
To get the min of x, subtract max c from min d
To get the max of x, subtract min c from max d
Therefore 0 < x < 2 ( important to note, x is not 0 and not 2)

From both these statements, we arrive at the conclusion that x could be a value strictly greater than 0 and strictly less than 2.

Now looking at answers, any option that lies in this range could be x and satisfy all data points in the table. Answer is Y, Y, N.

Additional explanation:
We cannot narrow down further based on the data given in the table. The only reason we checked for the second condition above is to find whether we can narrow down our range from the first condition (for example if d = 71 instead of 70 then 1 < x < 3 which combined with first would have given us 1 < x < 2).

We could have also skipped calculations for step 2, because the difference in rounded off values that are considered significant and insignificant are the same they would yield the same range of 0 to 2 (both not included).

A quick shortcut here is since values are rounded off within a range of 1 unit (slightly less than 1), we directly obtain the range by adding and subtracting 1 from the difference of rounded off values. Just be careful here to note that both extreme values are not included since range is slightly less than 1. If you are uncomfortable with this shortcut, above steps will always result in correct ranges.

To help understand the solution better, let’s assume a really small value of x and check for the above two data points. If it can satisfy these two it will satisfy any other data point.
For example Say x = 0.001, then possible values of a = 83.49, b = 83.5 meaning difference = 0.01 > x
And also c = 69.4999 and d = 69.5 meaning difference = 0.0001 < x

Even though you might consider a difference of 0.001 insignificant, we have no information on whether the author considers it significant or insignificant. We also have no information on the specific actual values so they could be anything within their own ranges that satisfy all the conditions. Therefore all values of 0 < x < 2 could be possible answers.

Here’s another example from the answer options, x = 1.4
Then possible values of a = 82.52, b = 84.13 meaning difference = 1.61 > x
and also c = 68.5 and d = 69.69 meaning difference = 1.19 < x

stackskillz · Answer

Alright this is a fun question. Definitely not easy, if you're seeing it for the first time, but definitely possible to solve.

Solution -  As per the solution of other's who have already pointed it out, for a difference of 1% between two columns, the range of values due to rounding error will be between 0 and 2. Extending the same principle for other values you get.

Difference   
   Range   
 
   -1  
  -2 < p < 1  
 
   0  
  -1 < p < 1  
 
   1  
  0 < p < 2  
 
   2  
  1 < p < 3  
 
   3  
  2 < p < 4

Here "p" represents the actual percentage difference.

Just focusing on the values in the 2014-15 column with significant difference, we get the following for the possible ranges for the percentage difference.

0 < p < 2 and 1 < p < 3.

The value of "x" to be chosen needs to be consistent with the value ranges of "p" such that "p" is significant as per the original table.

Therefore, the possible value range of x, would look like;

0 < x < p < 2.

soniasw16 · Answer

For 2013 to 2014, in Line 2, 2013 can be 71.5 and 2014 can be 69.4 which gives value of 2.1? Why is x = 2 not possible then?

Bunuel · Answer

Your 71.5 and 69.4 example makes that one row significant even if x = 2, but x must fit all rows at once. In 2014 to 2015 for prompt 5, the table shows 82 to 83 and it is marked significant. The largest raw difference consistent with rounding there is under 2, for example 83.49 minus 81.51 equals 1.98. Since it is significant, x must be less than 2. Hence x = 2 is impossible.

For each of three years and five survey prompts, the table shows the

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Prompt	2013	2014	2015	2013 to 2014	2014 to 2015
(1) I understand my organization.	63%	59%	61%	-	+
(2) I understand my role in the organization	72%	69	70%	-	.
(3) I am empowered to innovate.	58%	55%	57%	-	+
(4) My work is gratifying.	72%	70%	70%	-	.
(5) I am good at my job.	84%	82%	83%	-	+

Difference	Range
-1	-2 < p < 1
0	-1 < p < 1
1	0 < p < 2
2	1 < p < 3
3	2 < p < 4

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