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25 Aug 2020, 08:53
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B
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Difficulty:
95%
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Question Stats:
36% (02:26) correct
64%
(02:25)
wrong
based on 121
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b, c, d and e are positive integers. When b is divided by c, the quotient is d, and the remainder is e. What is the value of e?
(1) c = (b - e)/d
(2) 4c³ - 12c² + 8c = 0
(1) c = (b - e)/d
(2) 4c³ - 12c² + 8c = 0
25 Aug 2020, 11:00
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Question can be simplified to
b = cd + e
Now what is the value of e?
Option 1
This is another twisted version of the question stem itself.
Not sufficient.
Option 2
Solving the quadratic equation, the values of c comes out to be 0,1 or 2.
C cannot be 0.
C cannot be 1.
So c = 2.
Now if c = 2 then remainder has to be 1.
So e = 1.
Sufficient.
IMO the ans is B
Posted from my mobile device
b = cd + e
Now what is the value of e?
Option 1
This is another twisted version of the question stem itself.
Not sufficient.
Option 2
Solving the quadratic equation, the values of c comes out to be 0,1 or 2.
C cannot be 0.
C cannot be 1.
So c = 2.
Now if c = 2 then remainder has to be 1.
So e = 1.
Sufficient.
IMO the ans is B
Posted from my mobile device
25 Aug 2020, 13:29
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BrentGMATPrepNow
Given: b, c, d and e are positive integers. When b is divided by c, the quotient is d, and the remainder is e
Target question: What is the value of e?
Statement 1: c = (b - e)/d
The statement doesn't tell us anything. In fact it applies to ALL remainders. Here's what I mean:
There's a nice rule that says, If N divided by D equals Q with remainder R, then N = DQ + R
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
We're told that, when b is divided by c, the quotient is d, and the remainder is e.
When we apply the above property, we can write: b = cd + e, and this is what statement 1 is indirectly telling us.
Take: c = (b - e)/d
Multiply both sides of the equation by d to get: cd = b - e
Add e to both sides to get: cd + e = b
Since statement 1 provides no new information, it is NOT SUFFICIENT
Statement 2: 4c³ - 12c² + 8c = 0
Let's solve this equation for c.
Factor to get: 4c(c² - 3c + 2) = 0
Factor the quadratic to get: 4c(c - 1)(c - 2) = 0
So, the possible solutions are: c = 0, OR c = 1 OR c = 2
Let's examine all 3 cases:
c = 0: Since we're told that c is a POSITIVE integer, we know that c can't equal zero.
c = 1: Consider this important rule:
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Likewise, if c = 1, then the remainder (when b is divided by c) must be ZERO.
In other words, if c = 1, then e must equal 0 (according to the above rule)
Since we're told that e is a POSITIVE integer, we know that e cannot equal 0.
So, we can conclude that c can't equal 1.
By the process of elimination, we know that c = 2
If c = 2 then, according to the above rule, the remainder (e) must equal 0 or 1
However, since we're told that e is a POSITIVE integer, we know that e must equal 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
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