Terry had x dollars in her bank account at the beginning of a certain

Question

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

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Official Answer

D

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Archit3110 · Accepted Answer

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

MartyMurray · Answer

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).

chetan2u · Answer

If you work on the least and max possible value of b, the question becomes pretty simple.

let us write the events in order....
x......x+50......x+50-70.......x+50-70-40......x+50-70-40+80
x......x+50.........x-20...............x-60...................x+20

The max value is x+50, and the least value is x-60.  x-60\leq b\leq x+50 ... D gives the condition b ≥ x - 60.

OR we could check the option with the values we have

x......x+50.........x-20...............x-60...................x+20
If b is in the red portion, the option is not true.
A. b < x.............. Need not be true. ....... x......x+50......... x-20...............x-60................... x+20 
B. b = x + 20....... Need not be true  .......x......x+50.........x-20...............x-60................... x+20
C. b ≤ x + 40....... Need not be true .......x...... x+50......... x-20...............x-60...................x+20
D. b ≥ x - 60 ....... Always true .......x......x+50.........x-20...............x-60...................x+20
E. |x - b| ≤ 20.......x-20 ≤ b ≤ x+20  Need not be true .......x...... x+50......... x-20............... x-60................... x+20

D

sayan640 · Answer

KarishmaB   gmatophobia  Can you please explain this question ?

KarishmaB · Answer

Initial amount: x
After first transaction: x + 50
After second transaction: x - 20
After third transaction: x - 60
After fourth transaction: x + 20

The amount b at any given time could be less than or greater than or equal to x (before the first transaction)

A. b < x  
Could be but not necessary

B. b = x + 20  
Could be but not necessary. b could be x+ 50 or x - 20 etc.

C. b ≤ x + 40  
Not necessary. b could be x+ 50

D. b ≥ x - 60  
Correct. In all cases, the amount is > or = to (x - 60)

E. |x - b| ≤ 20  
The difference between x and b could be 50 or 60 too. Hence not necessary that it has to be less than equal to 20.

Answer (D)

Check out Inequalities and Absolute Values here: 
Inequalities:  https://youtu.be/VnEVS8kmWa8 
Absolute Values:  https://youtu.be/oqVfKQBcnrs

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Terry had x dollars in her bank account at the beginning of a certain

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