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# On a certain field trip, the ratio of teachers to students was 3 : 7.

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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14 Nov 2014, 08:57
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:42) correct 17% (01:47) wrong based on 170 sessions

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Tough and Tricky questions: Ratios.

On a certain field trip, the ratio of teachers to students was 3 : 7. What was the number of parents on the field trip?

(1) On the field trip, the ratio of the number of students to parents was 5 : 1.

(2) The number of parents on the trip was less than 20.

Kudos for a correct solution.

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Re: On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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14 Nov 2014, 10:32
1
1
statement 1: not sufficient
We still need to know either the total # of people or a value for one of the groups.

statement 2: not sufficient
We don't know the relationship between #of parents and #of students/teachers

Down to answers C or E.

Combined, we can use statement 1 to find the ratio of all the groups. Both ratios we are given have students. One value for students is 5 and the other is 7 so we multiple together to get 35. For every 35 students, there will then be 15 teachers and 7 parents. Using statement 2, we know that the # of parents is less than 20. With the ratios we are given, the # of parents can be 7 or 14. So we still do not have enough information to know for sure.

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Re: On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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15 Nov 2014, 01:20
1
Statement 1:
From question stem - The ratio of teachers(T) to students(S) was 3 : 7 => T/S = 3/7
From statement - The ratio of the number of students(S) to parents (P) was 5 : 1 => S/P = 5/1 => S = 5P
With the help of above two statements
T/5P = 3/7 => 7*T/15 =P ....... Not enough info
We don't know the number of teachers.

Insufficient. Hence option A & D are out.

Statement 2 :
The number of parents on the trip was less than 20 => P < 20
So,number of parents can be any number less than 20. 19,18,17 etc.

Insufficient. Hence option B is out.

By combining both the statements, we can't find number of parents.

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Re: On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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15 Nov 2014, 07:47
1
Statement 1 and 2 are clearly insufficient.

Combining both 1 and 2, we get

teacher : student: parents = 15:35:7

Therefore possible number of parents,which is less than 20, could either be 7 or 14.

Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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17 Nov 2014, 11:01
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Bunuel wrote:

Tough and Tricky questions: Ratios.

On a certain field trip, the ratio of teachers to students was 3 : 7. What was the number of parents on the field trip?

(1) On the field trip, the ratio of the number of students to parents was 5 : 1.

(2) The number of parents on the trip was less than 20.

Kudos for a correct solution.

Official Solution:

On a certain field trip, the ratio of teachers to students was 3 : 7. What was the number of parents on the field trip?

We need to determine the number of parents on a field trip. Since this problem involves three unknown quantities, we will assign each quantity a variable. The number of teachers, students, and parents will be $$t$$, $$s$$, and $$p$$, respectively. The problem tells us that $$t : s$$, the ratio of teachers to students, was 3 : 7.

Statement 1 tells us that $$s : p$$, the ratio of the number of students to parents, was 5 : 1. Since this ratio and the ratio in the prompt contain $$s$$, the number of students, then it is possible to create a ratio using all three variables by finding the least common multiple (LCM) of the two values for $$s$$.

The LCM of 7 and 5 is 35; multiply both ratios so that their $$s$$ term is 35. Thus, $$t : s = 3 : 7$$ becomes $$t : s = 15 : 35$$, and $$s : p = 5 : 1$$ becomes $$s : p = 35 : 7$$.

Combine the ratios to get $$t : s : p = 15 : 35 : 7$$.

This ratio gives us the relative quantities of teachers, students, and parents. However, any numbers of students, teachers, and parents that satisfy this ratio could have gone on the field trip. The numbers of teachers, students, and parents on the trip could have been 15, 35, and 7, respectively; they could also have been 30, 70, and 14. In fact, any multiple of this ratio would satisfy this statement. Statement 1 is therefore NOT sufficient. Eliminate answer choices A and D. The correct answer choice must be B, C, or E.

Statement 2 tells us that the number of parents on the field trip was less than 20. This does not allow us to identify the number of parents on the field trip; it could be anywhere between 0 or 19 and still satisfy the statement. This statement is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice is either C or E.

Taken together, the statements give us the relative amounts of all three quantities and place an upper bound on the number of parents: $$p \lt 20$$. However, as we saw in looking at statement 1, the first two multiples of our ratio both call for less than 20 parents. The possible values of $$p$$ are limited to 7 and 14, but there is not enough information to find a single value. Both statements together are NOT sufficient.

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Re: On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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27 Aug 2015, 02:28
let, teacher= t, students = s, parents = p
from stat-1
t:s = 3: 5 = 15 : 35
s:p = 5: 1 = 35 : 7
so, t : s : p = 15 : 35 : 7

we dont know the the number of teacher or students....insufficient.

from stat-2
the number of parents less than 20
we dont know the ratio for the parents

combinging stat 1 and 2
possible number of parents are 7 or 14.....still now inconclusive

ans : A
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Re: On a certain field trip, the ratio of teachers to students was 3 : 7.  [#permalink]

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26 Jan 2019, 07:20
Bunuel wrote:

Tough and Tricky questions: Ratios.

On a certain field trip, the ratio of teachers to students was 3 : 7. What was the number of parents on the field trip?

(1) On the field trip, the ratio of the number of students to parents was 5 : 1.

(2) The number of parents on the trip was less than 20.

Interesting question.
(1) On the field trip, the ratio of the number of students to parents was 5 : 1.
Just gives the ratio, this value can be 5:1 this wont give us the definite value

(2) The number of parents on the trip was less than 20.
No relation between students and parents, Nothing

Combine both the statements, we get a relationship among all three
T/S =3:7 -----Multiply the ratio by 5
S/P = 5: 1 -----Multiply the ratio by 7

T:S:P = 15 : 35 : 7

Now since parents are less than 20, the ratio can also be T:S:P = 30 : 70 :14

We are not getting a unique value

E
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Re: On a certain field trip, the ratio of teachers to students was 3 : 7.   [#permalink] 26 Jan 2019, 07:20
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