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11 Feb 2024, 07:29
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:37) correct
46%
(02:35)
wrong
based on 251
sessions
History
Date
Time
Result
Not Attempted Yet
On Tuesday, a nurse assisted in twice as many sonograms as x-rays. Was the amount of total time the nurse spent assisting with sonograms greater than the amount of time she spent assisting with x-rays?
(1) On Tuesday, the average (arithmetic mean) amount of time taken by the nurse to assist with an X-ray was 10 minutes more than the average time taken to assist with a sonogram.
(2) On Tuesday, the average amount of time taken by the nurse to assist with all sonograms and all x-rays combined was greater than 11 minutes.
(1) On Tuesday, the average (arithmetic mean) amount of time taken by the nurse to assist with an X-ray was 10 minutes more than the average time taken to assist with a sonogram.
(2) On Tuesday, the average amount of time taken by the nurse to assist with all sonograms and all x-rays combined was greater than 11 minutes.
13 Feb 2024, 10:35
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Official Explanation:
Let the number of sonograms be n
Let the number of x-rays be m
Let the average time taken by the nurse to assist with a sonogram be s
Let the average time taken by the nurse to assist with an x-ray be x
Since the nurse assisted in twice as many sonograms as x—rays, n = 2m (Equation I)
Total amount of time spent by the nurse to assist with sonograms = ns
Total amount of time spent by the nurse to assist with x-rays = mx
We need to find whether ns > mx
From Equation 1, this can also be expressed as: 2ms > mx
Cancelling “m” from both sides, we get: 2s > x
We need to find whether 2s > x
Statement (1)
x = s + 10 (Equation II)
Possibility 1: If s = 100, then x = 112 and 2s is greater than x.
Possibility 2: If s = 1, then x = 11 and 2s is NOT greater than x.
It is NOT possible to determine with certainty whether the total time spent by the nurse in assisting with sonograms was greater than the amount of time she spent assisting with x-rays. Hence, Statement (1) is insufficient.
Statement (2)
(ns+mx)/(n+m) > 11
(ns + mx) > 11(n + m)
From Equation I, we get: (2ms + mx) > 11(2m + m)
(2ms + mx) > 11(3m)
Cancelling “m” from both sides, we get: (2s + x) > 33 (Equation III)
Possibility 1: If s = 100 and x = 1, then 2s is greater than x.
Possibility 2: If s = 1 and x = 100, then 2s is NOT greater than x.
It is NOT possible to determine with certainty whether the total time spent by the nurse in assisting with sonograms was greater than the amount of time she spent assisting with x—rays. Hence, Statement (2) is insufficient.
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.
Statement (1) and Statement (2) combined
From Equation III; we get (2s + x) > 33
Substituting the value of “x” from Equation II in Equation III, we get;
2s + s + 10 > 33
3s + 10 > 33
3s > 23
s > 6.67
Possibility 1: If s = 7, then x = (s + 10) = 17. In this case, 2s is NOT greater than x.
Possibility 2: If s = 100, then x = (s + 10) = 110. In this case, 2s is greater than x.
It is NOT possible to determine with certainty whether the total time spent by the nurse in assisting with sonograms was greater than the amount of time she spent assisting with x-rays. Hence, Statement (1) and Statement (2) combined are insufficient.
E is the correct answer choice.
Let the number of sonograms be n
Let the number of x-rays be m
Let the average time taken by the nurse to assist with a sonogram be s
Let the average time taken by the nurse to assist with an x-ray be x
Since the nurse assisted in twice as many sonograms as x—rays, n = 2m (Equation I)
Total amount of time spent by the nurse to assist with sonograms = ns
Total amount of time spent by the nurse to assist with x-rays = mx
We need to find whether ns > mx
From Equation 1, this can also be expressed as: 2ms > mx
Cancelling “m” from both sides, we get: 2s > x
We need to find whether 2s > x
Statement (1)
x = s + 10 (Equation II)
Possibility 1: If s = 100, then x = 112 and 2s is greater than x.
Possibility 2: If s = 1, then x = 11 and 2s is NOT greater than x.
It is NOT possible to determine with certainty whether the total time spent by the nurse in assisting with sonograms was greater than the amount of time she spent assisting with x-rays. Hence, Statement (1) is insufficient.
Statement (2)
(ns+mx)/(n+m) > 11
(ns + mx) > 11(n + m)
From Equation I, we get: (2ms + mx) > 11(2m + m)
(2ms + mx) > 11(3m)
Cancelling “m” from both sides, we get: (2s + x) > 33 (Equation III)
Possibility 1: If s = 100 and x = 1, then 2s is greater than x.
Possibility 2: If s = 1 and x = 100, then 2s is NOT greater than x.
It is NOT possible to determine with certainty whether the total time spent by the nurse in assisting with sonograms was greater than the amount of time she spent assisting with x—rays. Hence, Statement (2) is insufficient.
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.
Statement (1) and Statement (2) combined
From Equation III; we get (2s + x) > 33
Substituting the value of “x” from Equation II in Equation III, we get;
2s + s + 10 > 33
3s + 10 > 33
3s > 23
s > 6.67
Possibility 1: If s = 7, then x = (s + 10) = 17. In this case, 2s is NOT greater than x.
Possibility 2: If s = 100, then x = (s + 10) = 110. In this case, 2s is greater than x.
It is NOT possible to determine with certainty whether the total time spent by the nurse in assisting with sonograms was greater than the amount of time she spent assisting with x-rays. Hence, Statement (1) and Statement (2) combined are insufficient.
E is the correct answer choice.
24 Jul 2024, 04:52
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____________avg time/procedure_____number_____total time
sonogram_____m____________________2a__________S
x-ray_________n_____________________a__________X
Question: Is S > X?
Statement 1: n = m + 10
S = 2a*m
X = a * (m+10) = am + 10a
=> Insufficient
Statement 2: S + X > 11
=> Insufficient
Combined:
S = 2*am
X = am + 10a
S + X = 3am + 10a > 11
=> Insufficient
Answer is E
sonogram_____m____________________2a__________S
x-ray_________n_____________________a__________X
Question: Is S > X?
Statement 1: n = m + 10
S = 2a*m
X = a * (m+10) = am + 10a
=> Insufficient
Statement 2: S + X > 11
=> Insufficient
Combined:
S = 2*am
X = am + 10a
S + X = 3am + 10a > 11
=> Insufficient
Answer is E
