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# k > j > 0

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1741 [0], given: 397

k > j > 0 [#permalink]  22 Nov 2017, 18:57
Expert's post
00:00

Question Stats:

63% (00:49) correct 36% (01:28) wrong based on 33 sessions
k > j > 0

 Quantity A Quantity B The time it takes to read k words at j words per minute The time it takes to read (k + 10) words at (j + 10) words per minute

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 9
Page: 522-523
[Reveal] Spoiler: OA

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Sandy
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Intern
Joined: 01 Sep 2017
Posts: 20
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Kudos [?]: 20 [1] , given: 21

Re: k > j > 0 [#permalink]  24 Nov 2017, 06:26
1
KUDOS
QTY A = K/J which basically could be any Number greater than 1
QTY B = K+10/J+10 which remains a number > 1. However it will become a smaller fraction. For instance (4/3) > (14/13).
Therefore A must be the answer.
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1741 [0], given: 397

Re: k > j > 0 [#permalink]  10 Dec 2017, 13:19
Expert's post
Explanation

Plug in numbers and use the rate formula—amount = rate × time—to check the quantities. If j = 1 and k = 2, then Quantity A is 2 minutes and Quantity B is $$\frac{20}{11}$$ minutes.

Quantity A is greater, so eliminate choices (B) and (C). Any acceptable set of values gives the same outcome; select choice A.
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Sandy
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Manager
Joined: 01 Nov 2018
Posts: 82
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Kudos [?]: 36 [1] , given: 20

Re: k > j > 0 [#permalink]  30 Dec 2018, 20:50
1
KUDOS
Expert's post
Always use this formula for work and rates.

W=rt

W= work, r= rate, t= time

this problem has k as units of work, and j and unit for rate, plug those in

K=jt
we are comparing this to
K+10= (J+10)t
we want to isolate time for each equation

for the first equation
K/j=t

for the second equation
(K+10)/(j+10) = t

now just plug in numbers
recall that K is greater than J,

Plug in K for 6 and 5 for j

then for the first equation
6/5=t

for the second equation

16/15=t

compare 6/5 and 16/15, you will see that 6/5 is greater,
Supreme Moderator
Joined: 01 Nov 2017
Posts: 349
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Kudos [?]: 98 [0], given: 2

Re: k > j > 0 [#permalink]  31 Dec 2018, 03:13
Expert's post
sandy wrote:
k > j > 0

 Quantity A Quantity B The time it takes to read k words at j words per minute The time it takes to read (k + 10) words at (j + 10) words per minute

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 9
Page: 522-523

So we are looking for $$\frac{k}{j}$$ and $$\frac{k+10}{j+10}$$ where k>j meaning $$\frac{k}{j}>1$$..
If we add the same positive number, which is 10 here, to both the numerator and denominator of a fraction >1, the new fraction with the higher numerator and denominator is lower..
For example... between 2/1 and (2+10)/(1+10)=12/11, 2/1 is bigger..

Check more on the same concepts from the following link
https://greprepclub.com/forum/effects-o ... 8a17db9825
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Manager
Joined: 22 Feb 2018
Posts: 156
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Kudos [?]: 94 [1] , given: 21

Re: k > j > 0 [#permalink]  06 Jan 2019, 15:34
1
KUDOS
0 < j < k
A: The time it takes to read k words at j words per minute
B: The time it takes to read (k + 10) words at (j + 10) words per minute
The only thing that we need is comparing fractions, disregarding the time (as time in both A and B is minute)
A: k /j
B: k+10 / j+10
If we have 1000/3 than we add 1000000 to both nominator and denominator, we will have:
1001000 / 1000003 which is going to 1, the more the added value is, the nearer the fraction is to 1.
By these we can say that k+10 / j+10 is nearer to 1 than k/j and as k is bigger than j, the fraction k/j is something more than 1, Thus, A is bigger than B.
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Re: k > j > 0   [#permalink] 06 Jan 2019, 15:34
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