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# Pat, Kate, and Mark charged a total of 162 hours to a

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Manager
Joined: 09 Feb 2006
Posts: 90
Location: Prague, CZ
Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 04:57
5
This post was
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Difficulty:

35% (medium)

Question Stats:

71% (01:49) correct 29% (01:41) wrong based on 530 sessions

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Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?

A. 18
B. 36
C. 72
D. 90
E. 108
[Reveal] Spoiler: OA
Manager
Joined: 09 Feb 2006
Posts: 90
Location: Prague, CZ
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 05:04
My solution was:

P=2K
P=(1/3)M

This gives a ratio 1:2:1/3, which is 3:6:1 (P:K:M).
TOTAL = 162 hours

According to the ratio it should be:
P=48,6 hours
K=97,2 hours
M=16,2 hours

----------------
TOTAL=48,6+97,2+16,2=162 hours
----------------
97,2-16,2=81 hours (which is not one of the choices)

Where is the mistake?
Manager
Joined: 20 Jun 2005
Posts: 147
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 05:24
M - K = ?

P + K + M = 162

P = 2K
P = 1/3 M <=> 3P = M

=> P + P/2 + 3P = 162
9P = 324
P=36

M - K = 3P - P/2 = 2,5 P = 90

Senior Manager
Joined: 08 Jun 2004
Posts: 491
Location: Europe
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 08:10
Another approach.

Let Mark be 'M' time on th project
Pat = 1/3M
Kate = 1/6M (as it twic less then Pat)

So 1/6M + 1/3M + M = 162 hours.
From here M = 108 hours, Kate = 18 hours
And the answer is 90 (108-18).

Very quick solution about 30 seconds.
Intern
Joined: 23 Jun 2006
Posts: 26
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 08:26
D.

P+K+M = 162

K = 1/2P
M = 3P

P+1/2P+3P = 162
P=36

K = 36/2 = 18
M = 3*36 = 108

108-18 = 90
SVP
Joined: 30 Mar 2006
Posts: 1727
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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05 Jul 2006, 02:20
B 36 hrs

P = 2K
M= 3P

P+K+M = 162
9P/2 = 162
P = 36
K = 72
M= 108

hence M-K = 36
Intern
Joined: 11 May 2004
Posts: 46
Location: USA
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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05 Jul 2006, 12:46
90

all u do is do

2:1:6=162 x= 18
36:18:108

108-18=90 D
VP
Joined: 02 Jun 2006
Posts: 1257
Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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05 Jul 2006, 14:30
(D) 90

Given p+m+k = 162

p = 2k
m =3p

m-k = ?

m-k = 3(2k) -k = 5k

=> m= 6k

i.e. 2k+k+6k = 162
i.e k= 162/9=18

m-k = 5k => 5x18 = 90.
VP
Joined: 17 Feb 2010
Posts: 1466

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20 Jul 2010, 09:39
You were in right direction.

Let Kate's hours be x.

Now, Pat Hours = 2 X Kate's Hours

therefore Pat Hours = 2x

Also, Pat Hours = 1/3 of Mark's Hours

Which is, Mark Hours = 3 x Pat Hours ==> 3 X (2x) ==> 6x

Given total hours = 162

so, x + 2x + 6x = 162

x = 18 which is Kate's Hours
Pat's Hours = 2x = 2 X 18 = 36
Mark's Hours = 6x = 6 X 18 = 108

Qustion is ==> how many more hours did Mark charge to the project than Kate?

Mark's Hours - Kate's Hours

108 - 18 = 90 Hours

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24 Mar 2011, 07:59
2
KUDOS
You may try my approach.
It may be easier and may be faster.

P+M+K=162
we need to find M-K

Lets Kate charged 60 hours
then Pat charged 60*2=120 hours
Mark charged 3 times more than Pat or 120*3=360

Total 60+120+360=540.
M-K= 360-60=300
Now look at the trick: We must have received 162 instead of 540 hours. and the difference (M-K) is 300 not one in the available answer choices.

Now guess what you need to do to obtain the correct answer choice? Exactly 162/540=3.33 , and 300/3.33=90.

hope it helps.
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Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
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06 May 2011, 09:26
2
KUDOS
P + K + M = 162

P = 2K, P = 1/3M

Hence K = 0.5P and M = 3P

P + 0.5 P + 3P = 162
or 4.5 P = 162

P = 18 * 2 = 36
K = 18
M = 108
M - K = 108 - 18 = 90

naveenhv wrote:
Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate
and 1/3 rd as much as Mark, how many more hours did mark charge to the project than Kate?

a) 18

b) 36

c) 72

d) 90

e) 108
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06 May 2011, 11:11
p,k and m are in the ratio 2:1 : 3

thus 6 x = 162
x = 27

mark hours = 27 *3 and kate hours = 27

thus difference = 27 *2 = 72
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Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
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06 May 2011, 11:18
The ratio is P : K : M = 2:1:6 and not 2:1:3
Hence 9y = 162
y = 18 (common factor)

Hence M-K = (6 - 1)y = 5y = 5 * 18 = 90

amit2k9 wrote:
p,k and m are in the ratio 2:1 : 3

thus 6 x = 162
x = 27

mark hours = 27 *3 and kate hours = 27

thus difference = 27 *2 = 72
Director
Joined: 01 Feb 2011
Posts: 703

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06 May 2011, 12:32
p + k + m =162

p = 2k
p = m/3
Solving we have m -k = 18*5 = 90

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Joined: 16 Nov 2010
Posts: 1589
Location: United States (IN)
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11 May 2011, 05:29
p + p/2 + 3p = 162

3p/2 + 3p = 162

p/2 + p = 54

p = 18 * 2 = 36

So M - K = 3p - p/2 = 108 - 18 = 90

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Joined: 23 Oct 2010
Posts: 375
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38

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15 Mar 2012, 09:42
1
KUDOS
p/a=2/1
p/m=1/3

p:a:m
2:1:-
2:-:6

p:a:m
2:1:6

2x+x+6x=162
x=18

(6-1)*18=90
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Joined: 01 Sep 2010
Posts: 3472
Re: Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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02 Jun 2012, 03:20
This problem is tricky and a bit time consuming. Maybe is a sub 600 level but under time pressure for me is 700 level (could be).

So: P+K+M=162

P=2k

P=1/3 M

k= 1/6 m by substitution

1/3m + 1/6 m + M = 162

9m = 972 -> m= 108

So M= 108 P = 36 and k = 18 how many more hou4rs and bla bla .....108 - 18 = 90

Straightforward.........
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02 Jun 2012, 03:22
LalaB wrote:
p/a=2/1
p/m=1/3

p:a:m
2:1:-
2:-:6

p:a:m
2:1:6

2x+x+6x=162
x=18

(6-1)*18=90

your approach have more style than mine. I like it. Nice
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Director
Joined: 24 Nov 2015
Posts: 584
Location: United States (LA)
Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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30 Apr 2016, 06:08
consider that Mark charges $$x$$ hours

so Pat charges $$\frac{x}{3}$$ hours

finally Kate charges $$\frac{x}{6}$$ hours

total of all three = $$\frac{3x}{2}$$ hours

but $$\frac{3x}{2}$$ = 162

x= 108 hours
difference between Mark and Kate = $$\frac{5x}{6}$$ hours

$$\frac{5x}{6}$$ = $$\frac{5}{6}$$ * 108 = 90 hours

SVP
Joined: 11 Sep 2015
Posts: 2051
Re: Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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20 Jan 2018, 07:22
Expert's post
Top Contributor
likar wrote:
Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?

A. 18
B. 36
C. 72
D. 90
E. 108

We can see that Kate charged the fewest hours, so...
Let x =the number of hours Kate charged

Pat charged twice as much time to the project as Kate
So, 2x = the number of hours Pat charged

Pat charged 1/3 as much times as Mark
In other words, Mark charged THREE TIMES as much time as Pat
So, 3(2x ) = the number of hours Mark charged
In other words, 6x = the number of hours Mark charged

Pat, Kate and Mark charged a total of 162 hours to a certain project.
We can write: x + 2x + 6x = 162
Simplify: 9x = 162
Solve: x = 18
So, Kate charged 18 hours
When we plug x = 18 into 6x, we see that Mark charged 108 hours

How many more hours did Mark charge to the project than Kate?
= 90
= D

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Re: Pat, Kate, and Mark charged a total of 162 hours to a   [#permalink] 20 Jan 2018, 07:22

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