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# Of the students in Tanner’s class, 8 wore a hat to school, 15 students

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BSchool Forum Moderator
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Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 08:53
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Question Stats:

59% (01:57) correct 41% (02:12) wrong based on 74 sessions

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Hey Guys
Need help with one -->

Of the students in Tanner’s class, 8 wore a hat to school, 15 students wore gloves, and 10 wore scarves. None of the students wore a scarf without gloves. Four students wore a hat, gloves, and a scarf. Half of the students who wore a hat also wore gloves. How many students are in Tanner’s class?

A)33
B)23
C)19
D)15
E) Cannot be determined.

NOTE -> This question is a part of KAPLAN and I just added the options to make it more GMAT-like.
[Reveal] Spoiler: OA

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Director
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Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 09:32
3
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stonecold wrote:
Hey Guys
Need help with one -->

Of the students in Tanner’s class, 8 wore a hat to school, 15 students wore gloves, and 10 wore scarves. None of the students wore a scarf without gloves. Four students wore a hat, gloves, and a scarf. Half of the students who wore a hat also wore gloves. How many students are in Tanner’s class?

A)33
B)23
C)19
D)15
E) Cannot be determined.

NOTE -> This question is a part of KAPLAN and I just added the options to make it more GMAT-like.

Students who wore hat $$= 8$$

Students who wore gloves $$= 15$$

Students who wore scarves $$= 10$$

All the students who wore scarves wore gloves. Students who wore both gloves and scarves $$= 10$$

Half of the students who wore a hat also wore gloves. Students who wore a hat also wore gloves $$= 4$$

Students wore a hat, gloves, and a scarf $$= 4$$

Out of $$10$$ Students who wore both gloves and scarves, $$4$$ of them wore hat, gloves and scarves.

Students who wore only gloves and scarves $$= 6$$

Therefore;

Students who wore only hat $$= 4$$

Students who wore only gloves $$= 5$$

Students who wore hat, gloves and scarves $$= 4$$

Students who wore only gloves and scarves $$= 6$$

Total number of students $$= 4 + 5 + 4+6 = 19$$

Hope its clear now.

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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 09:45
1
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TOTAL = A + B + C - ( SUM OF 2 - GROUP OVERLAPS ) + ( ALL 3 ) + NEITHER... WHEN U FILL ALL THESE QUANTITIES.. I SUPPOSE U DO NOT HAVE A CLEAR PICTURE OF WHAT IS REMAINING TO BE FILLED.. HENCE IMO E CAN NOT BE DETERMINED...

pardon me for the all caps.. and yes if this post helped you even an iota, kindly give kudos i require them to reach the next level... stuck without kudos at the silver level... pls pls pls kudos... beg u all

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Manager
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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 09:48
1
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thanks sashiim20 for your post on enligtening me on this questions...kudos given

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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 09:55
2
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sashiim20 wrote:
Students who wore hat $$= 8$$

Students who wore gloves $$= 15$$

Students who wore scarves $$= 10$$

All the students who wore scarves wore gloves. Students who wore both gloves and scarves $$= 10$$

Half of the students who wore a hat also wore gloves. Students who wore a hat also wore gloves $$= 4$$

Students wore a hat, gloves, and a scarf $$= 4$$

Out of $$10$$ Students who wore both gloves and scarves, $$4$$ of them wore hat, gloves and scarves.

Students who wore only gloves and scarves $$= 6$$

Therefore;

Students who wore only hat = 4

Students who wore only gloves $$= 5$$

Students who wore hat, gloves and scarves $$= 4$$

Students who wore only gloves and scarves $$= 6$$

Total number of students $$= 4 + 5 + 4+6 = 19$$

Hope its clear now.

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Hello bro,

I have a doubt your reasoning .... look at the highlighted part.

Students who wear hat as per the ques = 8 ( this includes people with only Hat, hat and scarf, hat and glove and hat scarf glove)

4 wear hats + glove+ scarf.

that leaves us with 4 people with hat ( this includes people with only Hat, hat and scarf, hat and glove). However, its given half of the people who wore hat also wore gloves. Thus 2 should wear Hat + Gloves and only 2 should remain with ONLY hat.

Although I shouldn't assume anything in GMAT, I can assume given the ques that hat and scarf =0 ----> Though I wouldn't assume that in exam.

I don't think this is a very GMAT like question.

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Director
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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 10:03
2
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gmatexam439 wrote:
sashiim20 wrote:
Students who wore hat $$= 8$$

Students who wore gloves $$= 15$$

Students who wore scarves $$= 10$$

All the students who wore scarves wore gloves. Students who wore both gloves and scarves $$= 10$$

Half of the students who wore a hat also wore gloves. Students who wore a hat also wore gloves $$= 4$$

Students wore a hat, gloves, and a scarf $$= 4$$

Out of $$10$$ Students who wore both gloves and scarves, $$4$$ of them wore hat, gloves and scarves.

Students who wore only gloves and scarves $$= 6$$

Therefore;

Students who wore only hat = 4

Students who wore only gloves $$= 5$$

Students who wore hat, gloves and scarves $$= 4$$

Students who wore only gloves and scarves $$= 6$$

Total number of students $$= 4 + 5 + 4+6 = 19$$

Hope its clear now.

_________________
Please Press "+1 Kudos" to appreciate.

Hello bro,

I have a doubt your reasoning .... look at the highlighted part.

Students who wear hat as per the ques = 8 ( this includes people with only Hat, hat and scarf, hat and glove and hat scarf glove)

4 wear hats + glove+ scarf.

that leaves us with 4 people with hat ( this includes people with only Hat, hat and scarf, hat and glove). However, its given half of the people who wore hat also wore gloves. Thus 2 should wear Hat + Gloves and only 2 should remain with ONLY hat.

Although I shouldn't assume anything in GMAT, I can assume given the ques that hat and scarf =0 ----> Though I wouldn't assume that in exam.

I don't think this is a very GMAT like question.

Hi gmatexam439,

Its not mentioned ONLY 4 students wear hats, gloves and scarves.

Given, 4 students wear hats, gloves and scarves. And half of students who wore hat also wore gloves (Which is = 4).

So 4 students who wear hats, gloves and scarves, also is included as students who wore hat and gloves.

Hence Students who wore only hat would be = 4.

Hope its clear now.

Kudos [?]: 274 [2], given: 261

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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 10:43
sashiim20 wrote:
Hi gmatexam439,

Its not mentioned ONLY 4 students wear hats, gloves and scarves.

Given, 4 students wear hats, gloves and scarves. And half of students who wore hat also wore gloves (Which is = 4).

So 4 students who wear hats, gloves and scarves, also is included as students who wore hat and gloves.

Hence Students who wore only hat would be = 4.

Hope its clear now.

Yup that makes sense. I thought this scenario as a second possibility; but since the ques says half of people who wear hat wear glove, its very ambiguous to divide 8 by 2 and say 4 wear only hat. Also, no info is given for hat + scarf.

I don't think such half baked ques will appear on gmat.

Thanks again for clearing my above doubt bro.
Regards

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Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 11:02
1
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stonecold wrote:
Hey Guys
Need help with one -->

Of the students in Tanner’s class, 8 wore a hat to school, 15 students wore gloves, and 10 wore scarves. None of the students wore a scarf without gloves. Four students wore a hat, gloves, and a scarf. Half of the students who wore a hat also wore gloves. How many students are in Tanner’s class?

A)33
B)23
C)19
D)15
E) Cannot be determined.

Attachment:

HGSVenn.jpg [ 53.78 KiB | Viewed 766 times ]

I had to use this Venn diagram. Maybe it will help, because this problem is sneaky.

Hats = 8
Gloves = 15
Scarves = 10
H + G + S = 4

None of the students wore a scarf without gloves
Half of the students who wore a hat also wore gloves = 4

1. Start with most restrictive information, H + G + S = 4. Put 4 in the triple overlap (blue).

Next two most restrictive conditions, one at a time.

2. None of the students wore a scarf without gloves. If they had scarves on, they had gloves on, too.

So: ZERO students will wear scarves only. Put 0 in the yellow part.

ZERO of the students will wear scarves and hats only. Put 0 in H + S (purple)

And: if S, then G at least means S + G = 10. However, blue affects everything else. Blue is H + G + S.

S + G (green) looks very tempting in which to put S + G = 10 -- but the blue segment already has 4 of the 10 students who wore S and G.
10 - 4 = 6. Put 6 in S + G (green).

3. Half of the students who wore a hat also wore gloves, half = 4

Now G + H looks tempting. Check blue first. There are 4 students with H + G + S. This condition is covered.
Put 0 in G + H.

4. Final calculations: H only and G only

H only - every intersection around H only is filled with a number (white, blue, purple). Add them up. 0 + 0 + 4 = 4. Total H = 8.
8 - 4(in blue) = 4. Put 4 in H only.

G only - every intersection around G only is filled. Add the intersecting parts' (white, blue, green) numbers up: 0 + 4 + 6 = 10
Total G = 15. (15 - 10) = 5 in G only.

Now add every value (when you've diagrammed, it's different from the formula, because the diagram accounts for all the things you would have to add or subtract twice or whatever).

Leaving out zeros: 5 + 6 + 4 + 4 = 19

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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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13 Aug 2017, 21:32
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Let students who wore hats be denoted by P(H)
Let students who wore gloves be denoted by P(G)
Let students who wore scarves be denoted by P(S)

P(Total) = P(H) + P(G) + P(S) - P(Only 2) - 2*P(All 3)

Given data:
P(H) = 8
P(G) = 15
P(S) = 10
P(All 3) = 4

We can get the following information from the question stem
None of the students wore a scarf without gloves
P(S & G) = 10 - 4(who have all 3) = 6
Half of the students who wore a hat also wore gloves
P(H & G) = $$\frac{P(H)}{2}$$ - 4(who have all 3) = $$\frac{8}{2} - 4 = 0$$
Similarly P(S & H) = 0

P(Only 2) = P(S & G) + P(H & G) + P(S & H) = 6+0+0 = 6

Therefore, the number of students in Tanner's class :
P(Total) = 8 + 15 + 10 - 6 - 2*(4) = 33 - 14 = 19(Option C)

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Re: Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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15 Aug 2017, 06:44
genxer123 wrote:
stonecold wrote:
Hey Guys
Need help with one -->

Of the students in Tanner’s class, 8 wore a hat to school, 15 students wore gloves, and 10 wore scarves. None of the students wore a scarf without gloves. Four students wore a hat, gloves, and a scarf. Half of the students who wore a hat also wore gloves. How many students are in Tanner’s class?

A)33
B)23
C)19
D)15
E) Cannot be determined.

Attachment:
HGSVenn.jpg

I had to use this Venn diagram. Maybe it will help, because this problem is sneaky.

Hats = 8
Gloves = 15
Scarves = 10
H + G + S = 4

None of the students wore a scarf without gloves
Half of the students who wore a hat also wore gloves = 4

1. Start with most restrictive information, H + G + S = 4. Put 4 in the triple overlap (blue).

Next two most restrictive conditions, one at a time.

2. None of the students wore a scarf without gloves. If they had scarves on, they had gloves on, too.

So: ZERO students will wear scarves only. Put 0 in the yellow part.

ZERO of the students will wear scarves and hats only. Put 0 in H + S (purple)

And: if S, then G at least means S + G = 10. However, blue affects everything else. Blue is H + G + S.

S + G (green) looks very tempting in which to put S + G = 10 -- but the blue segment already has 4 of the 10 students who wore S and G.
10 - 4 = 6. Put 6 in S + G (green).

3. Half of the students who wore a hat also wore gloves, half = 4

Now G + H looks tempting. Check blue first. There are 4 students with H + G + S. This condition is covered.
Put 0 in G + H.

4. Final calculations: H only and G only

H only - every intersection around H only is filled with a number (white, blue, purple). Add them up. 0 + 0 + 4 = 4. Total H = 8.
8 - 4(in blue) = 4. Put 4 in H only.

G only - every intersection around G only is filled. Add the intersecting parts' (white, blue, green) numbers up: 0 + 4 + 6 = 10
Total G = 15. (15 - 10) = 5 in G only.

Now add every value (when you've diagrammed, it's different from the formula, because the diagram accounts for all the things you would have to add or subtract twice or whatever).

Leaving out zeros: 5 + 6 + 4 + 4 = 19

This is the most clear explanation. Thanks for sharing.

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Of the students in Tanner’s class, 8 wore a hat to school, 15 students [#permalink]

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15 Aug 2017, 20:29
Drealnapster wrote:

This is the most clear explanation. Thanks for sharing.

It's nice to get feedback. You're very welcome.

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Of the students in Tanner’s class, 8 wore a hat to school, 15 students   [#permalink] 15 Aug 2017, 20:29
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