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A science lab is conducting an experiment monitoring the appearance of

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Math Expert
Joined: 02 Sep 2009
Posts: 58391
A science lab is conducting an experiment monitoring the appearance of  [#permalink]

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31 Mar 2017, 04:00
3
7
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Difficulty:

45% (medium)

Question Stats:

64% (01:58) correct 36% (02:27) wrong based on 158 sessions

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A science lab is conducting an experiment monitoring the appearance of genetic traits in laboratory rats. Of the three traits being monitored all of the animals bear at least one of the three traits being monitored, one third of the rats were obese, three fourths of the rats had white fur, and one half of the rats had an elongated mandible. How many had all three of these traits?

(1) Of the 120 rats in the experiment, 40 had white fur and an elongated mandible.
(2) Of the 120 rats in the experiment, 40 had exactly two of the traits.

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Joined: 21 Jul 2017
Posts: 187
Location: India
GMAT 1: 660 Q47 V34
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WE: Project Management (Education)
Re: A science lab is conducting an experiment monitoring the appearance of  [#permalink]

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05 Oct 2017, 09:45
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2
A useful formula for 3 overlapping groups:

T = A + B + C - (AB + AC + BC) - 2(ABC)

The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of the groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.

In the problem above:
Let T = 120.
Obese = (1/3)(120) = 40.
White fur = (3/4)(120) = 90.
Elongated mandible = (1/2)(120) = 60.
Exactly 2 of the groups = OW + OE + WE.
All 3 groups = OWE.

Plugging these values into the formula, we get:
120 = 40 + 90 + 60 - (OW + OE + WE) - 2(OWE)
-70 = - (OW + OE + WE) - 2(OWE)
(OW + OE + WE) + 2(OWE) = 70.

Since the least possible value for (OW + OE + WE) is 0, the greatest possible value for OWE is 35.

Statement 1:
Of the 120 rats in the experiment, 40 had white fur and an elongated mandible.
Case 1: Of these 40 rats, 5 have all 3 traits (OWE=5), implying that 35 have only white fur and an elongated mandible (WE=35).
Case 2: Of these 40 rats, 10 have all 3 traits (OWE=10), implying that 30 have only white fur and an elongated mandible (WE=30).
Since OWE can be different values, INSUFFICIENT.

Statement 2:
Of the 120 rats in the experiment, 40 had exactly two of the traits.
Substituting (OW + OE + WE) = 40 into (OW + OE + WE) + 2(OWE) = 70, we get:
40 + 2(OWE) = 70.
2(OWE) = 30
OWE = 15.
SUFFICIENT.

General Discussion
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: A science lab is conducting an experiment monitoring the appearance of  [#permalink]

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31 Mar 2017, 22:28
2
Number of 3 overlaps = ?

Exactly one + Exactly two overlaps + Exactly 3 overlaps = 120 -------(1)
Exactly one + 2(Exactly two overlaps) + 3(Exactly 3 overlaps) = 40 + 90 + 60 = 190 -------(2)
(2) - (1) = Exactly two overlaps + 2(Exactly 3 overlaps) = 70
To find the number of 3 overlaps we need the value of exactly two overlaps.

St1: Of the 120 rats in the experiment, 40 had white fur and an elongated mandible. --> Not Sufficient as we do not know the overlaps between white fur and obese, and between obese and elongated mandible.

St2: Exactly two overlaps = 40 --> 3 overlaps = (70 - 40)/2 = 15.
Sufficient.

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Re: A science lab is conducting an experiment monitoring the appearance of  [#permalink]

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13 Oct 2018, 05:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A science lab is conducting an experiment monitoring the appearance of   [#permalink] 13 Oct 2018, 05:13
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