GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Feb 2019, 19:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# A school has a students and b teachers

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Apr 2018
Posts: 41
GMAT 1: 750 Q50 V41
A school has a students and b teachers  [#permalink]

### Show Tags

09 Sep 2018, 08:37
1
00:00

Difficulty:

95% (hard)

Question Stats:

27% (02:34) correct 73% (02:41) wrong based on 61 sessions

### HideShow timer Statistics

A school has a students and b teachers. If a < 150, b < 25, and classes have a maximum of 15 students, can the a students
be distributed among the b teachers so that each class has the same number of students? (Assume that any student can be
taught by any teacher)

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

(2) The greatest common factor of a and b is 10
Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
A school has a students and b teachers  [#permalink]

### Show Tags

Updated on: 09 Sep 2018, 09:44
1
alphak3nny001 wrote:
A school has a students and b teachers. If a < 150, b < 25, and classes have a maximum of 15 students, can the a students
be distributed among the b teachers so that each class has the same number of students? (Assume that any student can be
taught by any teacher)

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

(2) The greatest common factor of a and b is 10

Here is my take on this .

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15
we have to find LCM of the given numbers
We therefore have 90 students

case 1
say number of teachers = 15 (b<25)
then yes students can be evenly distributed

case 2
when no of teachers = 24
then no

(2) The greatest common factor of a and b is 10
a and b can be 100 and 10
or
$$90 and 20$$
or
90 and 10

insufficient

using both still insufficient

E

Originally posted by CounterSniper on 09 Sep 2018, 09:01.
Last edited by CounterSniper on 09 Sep 2018, 09:44, edited 1 time in total.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 763
Re: A school has a students and b teachers  [#permalink]

### Show Tags

09 Sep 2018, 11:13
alphak3nny001 wrote:
A school has A students and B teachers. If A < 150, B < 25, and classes have a maximum of 15 students, can the A students be distributed among the B teachers so that each class has the same number of students? (Assume that any student can be taught by any teacher, any class has exactly one teacher associated with it.)

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

(2) The greatest common factor of A and B is 10

$$2 \leqslant A \leqslant 149\,\,\,\operatorname{int} \,\,\,\,\left( * \right)\,\,\,\,\left( {A\,\, = \,\,\# \,\,{\text{students}}} \right)$$

$$2 \leqslant B \leqslant 24\,\,\,\operatorname{int} \,\,\,\,\,\,\,\,\,\left( {B\,\, = \,\,\# \,\,{\text{classes}}\,\,{\text{ = }}\,\,\,\# \,\,{\text{teachers}}} \right)$$

$$\left( {\frac{{n\,\,{\text{students}}}}{{1\,\,\,{\text{class}}}}} \right)\,\,\,\left( {B\,\,{\text{classes}}} \right)\,\,\,\mathop = \limits^? \,\,A\,\,\,\mathop \Leftrightarrow \limits^{1\,\, \leqslant \,\,n\,\,\operatorname{int} \,\, \leqslant \,\,15} \,\,\,\,\,\boxed{\,\,?\,\,\,\,:\,\,\,\,1 \leqslant \,\,\frac{A}{B}\,\,\, = \,\,\operatorname{int} \,\, \leqslant 15\,\,\,}$$

$$\left( 1 \right) \cap \left( * \right)\,\,\,\left\{ \begin{gathered} A\,\,{\text{is}}\,\,{\text{a}}\,\,{\text{multiple}}\,\,{\text{of}}\,\,LCM\left( {2,3,5,6,9,10,15} \right) = 90 \hfill \\ \left( * \right)\,\,\,\,2 \leqslant A \leqslant 149 \hfill \\ \end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,A = 90$$

$$\left( {1 + 2} \right) \cap \left( * \right)\,\,\,\left\{ \begin{gathered} A = 90\,\,\,\,\,;\,\,\,\,\,2 \leqslant B \leqslant 24\,\,\,\operatorname{int} \,\,\, \hfill \\ GCD\left( {A,B} \right) = 10 \hfill \\ \end{gathered} \right.$$

$$\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {{\text{A,B}}} \right) = \left( {90,10} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left( {\frac{{90}}{{10}} = 9} \right) \hfill \\ \,{\text{Take}}\,\,\left( {{\text{A,B}}} \right) = \left( {90,20} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\left( {\frac{{90}}{{20}} \ne \operatorname{int} } \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{INSUFF}}.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

SVP
Joined: 26 Mar 2013
Posts: 2067
Re: A school has a students and b teachers  [#permalink]

### Show Tags

09 Sep 2018, 13:18
alphak3nny001 wrote:
A school has a students and b teachers. If a < 150, b < 25, and classes have a maximum of 15 students, can the a students
be distributed among the b teachers so that each class has the same number of students? (Assume that any student can be
taught by any teacher)

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

(2) The greatest common factor of a and b is 10

The question asks if we can evenly divide the students into classes.

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

The least common multiple =90 students

The number teachers < 25

Let b= 20

$$\frac{a}{b}=\frac{90}{20}=\frac{9}{2}$$.............Answer is No

Let b= 10

$$\frac{a}{b}=\frac{90}{10}=\frac{9}{1}$$.............Answer is yes

Insufficient

(2) The greatest common factor of a and b is 10

Use same examples above

Let a=90 & b=20

Let a=90 & b=10

Insufficient

Combine 1 & 2

Use same examples above........No conclusive answer

Insufficient

Manager
Joined: 04 Oct 2017
Posts: 79
Re: A school has a students and b teachers  [#permalink]

### Show Tags

09 Sep 2018, 18:58
Mo2men wrote:
alphak3nny001 wrote:
A school has a students and b teachers. If a < 150, b < 25, and classes have a maximum of 15 students, can the a students
be distributed among the b teachers so that each class has the same number of students? (Assume that any student can be
taught by any teacher)

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

(2) The greatest common factor of a and b is 10

The question asks if we can evenly divide the students into classes.

(1) It is possible to divide the students evenly into groups of 2, 3, 5, 6, 9, 10, or 15

The least common multiple =90 students

The number teachers < 25

Let b= 20

$$\frac{a}{b}=\frac{90}{20}=\frac{9}{2}$$.............Answer is No

Let b= 10

$$\frac{a}{b}=\frac{90}{10}=\frac{9}{1}$$.............Answer is yes

Insufficient

(2) The greatest common factor of a and b is 10

Use same examples above

Let a=90 & b=20

Let a=90 & b=10

Insufficient

Combine 1 & 2

Use same examples above........No conclusive answer

Insufficient

Hi,

I have a doubt. When we combine the statements. 90/20 is not a whole number. Hence we can eliminate it and 90/10 could be the solution. Please clarify.
Re: A school has a students and b teachers   [#permalink] 09 Sep 2018, 18:58
Display posts from previous: Sort by