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

Question

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

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

pranto · Answer

the answer should be 16. 
30-(7+3+4) = 16.
Answer D.

theLucifer · Answer

Only P = All P - ( P&T + P&V + P&V&T)
=30-(4+7+3)
=30-(14)
16

Ans  (D)

generis · Answer

2018-06-05vennvests.png 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.

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

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

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