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04 Jan 2024, 04:34
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Terry had x dollars in her bank account at the beginning of a certain week. During the week, four transactions were recorded in her account in the following order: a deposit of $50, a withdrawal of $70, a withdrawal of $40, and a deposit of $80. If b represents the amount in Terry's account at some time during the week, which of the following must be true?
A. b < x
B. b = x + 20
C. b ≤ x + 40
D. b ≥ x - 60
E. |x - b| ≤ 20
TERRY.png [ 57.34 KiB | Viewed 8469 times ]
A. b < x
B. b = x + 20
C. b ≤ x + 40
D. b ≥ x - 60
E. |x - b| ≤ 20
Attachment:
TERRY.png [ 57.34 KiB | Viewed 8469 times ]
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05 Jan 2024, 08:28
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let x be $ 100
then we have 4 events happening
such that value of b will be
1. 150
2. 80
3 40
4 . 120
range of b is
39.9<=b<=151.1
from given options we know x is 100
option D is correct b ≥ x - 60
then we have 4 events happening
such that value of b will be
1. 150
2. 80
3 40
4 . 120
range of b is
39.9<=b<=151.1
from given options we know x is 100
option D is correct b ≥ x - 60
Churej
Updated on: 05 Jan 2024, 17:25
Originally posted by MartyMurray on 04 Jan 2024, 12:29.
Last edited by MartyMurray on 05 Jan 2024, 17:25, edited 1 time in total.
Last edited by MartyMurray on 05 Jan 2024, 17:25, edited 1 time in total.
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Terry had x dollars in her bank account at the beginning of a certain week. During the week, four transactions were recorded in her account in the following order: a deposit of $50, a withdrawal of $70, a withdrawal of $40, and a deposit of $80. If b represents the amount in Terry's account at some time during the week, which of the following must be true?
This question is relatively simple. At the same time, it is a little tricky because of two aspects of it.
The first tricky aspect is that we aren't concerned with only the value of b at the end of the week. We have to consider the possible value of b "at some time during the week."
The second tricky aspect is that the correct answer is not something that just COULD be true. It's something that MUST be true. So, to get this question correct, we have to eliminate the choices that could be true but aren't necessarily true and find the choice that must be true.
A. b < x
This choice could be true. After all, after the first two transactions, b = x + 50 - 70 = x - 20. So, after the first two transactions, b < x.
However, this choice isn't necessarily true since, after the first transaction, b = x + 50. In that case, b > x.
Eliminate.
B. b = x + 20
This choice could be true. After all, at the end of the week, b = x + 50 - 70 - 40 + 80 = x + 20.
However, this choice isn't necessarily true since, at other points during the week b ≠ x + 20.
Still, many people choose this choice, probably because x + 20 is the final value of b at the end of the week. To avoid choosing a trap like this one, we have to keep in mind exactly what is the question that we need to answer.
Eliminate.
C. b ≤ x + 40
This choice could be true. After all, after any of the transactions after the first transactions, b ≤ x + 40.
Here's the progression of the value of b: x, x + 50, x - 20, x - 60, x + 20
However, this choice isn't necessarily true since, after the first transaction, b = x + 50
Eliminate.
D. b ≥ x - 60
This choice must be true. After all, the value of b is lowest after the first three transactions, when b = x + 50 - 70 - 40 = b - 60
So, during the entire week, b ≥ x - 60.
Keep.
E. |x - b| ≤ 20
This choice could be true. After all, at the end of the week, b = x + 50 - 70 - 40 + 80 = x + 20. So, |x - b| = |-20| = 20
However, this choice is not necessarily true since, at other points during the week, the absolute difference between x and b is greater than 20. For instance, after the first transaction, b = x + 50. So, |x - b| = 50 > 20.
Eliminate.
The correct answer is (D).
This question is relatively simple. At the same time, it is a little tricky because of two aspects of it.
The first tricky aspect is that we aren't concerned with only the value of b at the end of the week. We have to consider the possible value of b "at some time during the week."
The second tricky aspect is that the correct answer is not something that just COULD be true. It's something that MUST be true. So, to get this question correct, we have to eliminate the choices that could be true but aren't necessarily true and find the choice that must be true.
A. b < x
This choice could be true. After all, after the first two transactions, b = x + 50 - 70 = x - 20. So, after the first two transactions, b < x.
However, this choice isn't necessarily true since, after the first transaction, b = x + 50. In that case, b > x.
Eliminate.
B. b = x + 20
This choice could be true. After all, at the end of the week, b = x + 50 - 70 - 40 + 80 = x + 20.
However, this choice isn't necessarily true since, at other points during the week b ≠ x + 20.
Still, many people choose this choice, probably because x + 20 is the final value of b at the end of the week. To avoid choosing a trap like this one, we have to keep in mind exactly what is the question that we need to answer.
Eliminate.
C. b ≤ x + 40
This choice could be true. After all, after any of the transactions after the first transactions, b ≤ x + 40.
Here's the progression of the value of b: x, x + 50, x - 20, x - 60, x + 20
However, this choice isn't necessarily true since, after the first transaction, b = x + 50
Eliminate.
D. b ≥ x - 60
This choice must be true. After all, the value of b is lowest after the first three transactions, when b = x + 50 - 70 - 40 = b - 60
So, during the entire week, b ≥ x - 60.
Keep.
E. |x - b| ≤ 20
This choice could be true. After all, at the end of the week, b = x + 50 - 70 - 40 + 80 = x + 20. So, |x - b| = |-20| = 20
However, this choice is not necessarily true since, at other points during the week, the absolute difference between x and b is greater than 20. For instance, after the first transaction, b = x + 50. So, |x - b| = 50 > 20.
Eliminate.
The correct answer is (D).
