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Forty-four men are at a party and they all are wearing ties, vests, pe

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Bunuel
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Forty-four men are at a party and they all are wearing ties, vests, pe [#permalink] New post   21 Dec 2016, 04:56
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Forty-four men are at a party and they all are wearing ties, vests, penny-loafers, or combination of the three. Twenty of the men are wearing ties, 30 of the men are wearing vests and 4 men are wearing only these two. If 13 of the men are wearing a only tie and penny loafers, 7 men are wearing only a vest and penny-loafers, and 3 men are wearing all three, how many men are wearing only a vest?

A. 3
B. 12
C. 13
D. 16
E. 27
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pranto
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Re: Forty-four men are at a party and they all are wearing ties, vests, pe [#permalink] New post   26 Dec 2016, 21:57
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the answer should be 16.
30-(7+3+4) = 16.
Answer D.
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Re: Forty-four men are at a party and they all are wearing ties, vests, pe [#permalink] New post   27 Dec 2016, 03:00
Only P = All P - ( P&T + P&V + P&V&T)
=30-(4+7+3)
=30-(14)
16

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generis
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Forty-four men are at a party and they all are wearing ties, vests, pe [#permalink] New post   05 Jun 2018, 15:37
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Bunuel wrote:
Forty-four men are at a party and they all are wearing ties, vests, penny-loafers, or combination of the three. Twenty of the men are wearing ties, 30 of the men are wearing vests and 4 men are wearing only these two. If 13 of the men are wearing a only tie and penny loafers, 7 men are wearing only a vest and penny-loafers, and 3 men are wearing all three, how many men are wearing only a vest?

A. 3
B. 12
C. 13
D. 16
E. 27

Attachment:
2018-06-05vennvests.png
2018-06-05vennvests.png [ 50.13 KiB | Viewed 1854 times ]

Venn diagram works well here.

Ties, T = 20
Vests, V = 30
Penny loafers, P = ?
T + V = 4
T + P = 13
V + P = 7
all 3 = 3

Only information in blue is needed, though I think the
Venn diagram makes that fact easier for some people to see.

1) Most restrictive first: "All 3" = 3, in pink area
2) Gray overlap #1: T + V = 4
3) Gray overlap #2: V + P = 7
4) Areas of overlap in which that are parts of V total =
gray + gray + pink = 4 + 3 + 7 = 14
5) Total vests: 30. ONLY vests = TOTAL - Overlap = (30 - 14) = 16

Answer D

Information that does not matter is in dark gray
type on the left side of the diagram.
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Forty-four men are at a party and they all are wearing ties, vests, pe [#permalink]
05 Jun 2018, 15:37
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