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VB = 3V + 14B

Clearing V:
VB-3V = 14B
V*(B-3) = 14B
V = 14B/(B-3) = (14B-42+42)/(B-3) = 14+42/(B-3)

42=2*3*7
factors: 1,2,3,6,7,14,21,42

B < 15
B-3 < 12
B in (4,5,6,9,10)

B=4, V=56, V+B=60
B=5, V=35, V+B=40
B=6, V=28, V+B=34
B=9, V=21, V+B=30
B=10, V=20, V+B=30

36 is not in the list

Answer C
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Let v - number of vans = > students carried by vans = 3v
let b - number of busses => students carried by busses = 14b

Total students = 3v+14b and vb = > 3v + 14b = vb
3v - vb = -14b. rearranging to get v in terms of b

v = 14b/(3-b)
b cannot be less than or equal to 3 (or we get -ve number of vans)

substituting values b = 4, we get v = 60
b = 5, v = 40
b =6, v = 28
b = 7, v = 49/4 (Not possible)
b = 8, v = 112/5 (not possible)
b = 9, v = 21
b = 10, v = 20
b = 11, v = 77/4 (not possible)
b = 12, v = 56/3 (Not possible)
b = 13, v = 91/5 (not possible)
b = 14, v = 20

Comparing b+v values with the answers, we do not get 36 anywhere.

Answer C
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3*van+14*bus = van*bus

(bus-3)*van = 14*bus
van = 14*bus/(bus-3)

bus<=14 and van must be an integer.

bus=14 -> van no integer
bus=13 -> van no integer
bus=12 -> van no integer
bus=11 -> van no integer
bus=10 -> van=20 -> bus+van=30
bus=9 -> van=21 -> bus+van=30
bus=8 -> van no integer
bus=7 -> van no integer
bus=6 -> van=28 -> bus+van=34
bus=5 -> van=35 -> bus+van=40
bus=4 -> van=56 -> bus+van=60

bus+van can be 30,34,40,60

36 is the answer

The answer is C
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number of students = 3v + 14b = vb with b<=14

14b = vb - 3v
14b = v(b - 3)
14b - 3*14 + 3*14 = v(b - 3)
14(b - 3) + 42 = v(b - 3)
v = 14 + 42/(b - 3)

42 must be divisible by (b-3)

this happens when b is 4,5,6,9 and 10

v is 56,35,28,21 and 20 respectively

v+b is 60,40,34,30 and 30 respectively

36 is not in the options

The correct answer is C
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Option C - 36
sol
Van carries student =3 v
Bus carries student =14 b

So vb= 3v+14b
Solving for v
v(b-3)=14b
v=14b/b-3 = 14 + 42/b-3

For positive integer b-3 must be divisible by 42
so possible values are = 1,2,3,4,7,14,21
and B>3 and B<15
so values for b can be - 4,5,6,9,10

So if b 4 then b-3= 1 , 42 and v= 56 , V+B= 60
B -5 , B-3 =2 , 42/(b-3)= 21 , v= 40 V+B=40
B is 6 , B-3= 3 , 14 , v= 28 V+B= 34
B is 9 , B-3 =6 , v = 21 V+B =30
B is 10 , B-3 =7 , v=20 V+B=30

We donot have 36 as the value so 36 is the ans







Bunuel
A school used only vans and buses to transport students on a field trip. Each van carried exactly 3 students, and each bus carried exactly 14 students. The number of vans used, when multiplied by the number of buses used, was equal to the total number of students transported. If fewer than 15 buses were used, which of the following could NOT be the total number of vehicles used?

A. 30
B. 34
C. 36
D. 40
E. 60


 


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Bunuel
A school used only vans and buses to transport students on a field trip. Each van carried exactly 3 students, and each bus carried exactly 14 students. The number of vans used, when multiplied by the number of buses used, was equal to the total number of students transported. If fewer than 15 buses were used, which of the following could NOT be the total number of vehicles used?

A. 30
B. 34
C. 36
D. 40
E. 60


 


This question was provided by GMAT Club
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Let vans = v and buses = b.

The total number of students is: 3v + 14b

We're told this is equal to:

v * b So: vb = 3v + 14b

vb - 3v - 14b = 0

(v - 14)(b - 3) = 42

Since fewer than 15 buses were used,

b < 15, so b - 3 < 12.

Factor pairs of 42 where the smaller factor can be b - 3:

1 × 42 = vehicles = 4 + 56 = 60

2 × 21 = vehicles = 5 + 35 = 40

3 × 14 = vehicles = 6 + 28 = 34

6 × 7 = vehicles = 9 + 21 = 30

7 × 6 = vehicles = 10 + 20 = 30

Possible totals are: 30, 34, 40, 60

36 never appears.

Option C
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Ans is 36

3x + 14 y = xy

and y <15 1 to 14 only total x+y = 36 not possible I did hit and trial to get and at last left with 34 & 36 then 34 can be 6 & 28 so 36 is the NOT possible
Bunuel
A school used only vans and buses to transport students on a field trip. Each van carried exactly 3 students, and each bus carried exactly 14 students. The number of vans used, when multiplied by the number of buses used, was equal to the total number of students transported. If fewer than 15 buses were used, which of the following could NOT be the total number of vehicles used?

A. 30
B. 34
C. 36
D. 40
E. 60


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
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