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

 It is currently 17 Oct 2019, 16:08

### 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

# A competition requires teams to attempt 10 long jumps and 5 high jumps

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58402
A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

02 Sep 2019, 23:14
00:00

Difficulty:

25% (medium)

Question Stats:

82% (02:52) correct 18% (02:10) wrong based on 17 sessions

### HideShow timer Statistics

Competition Mode Question

A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?

(A) 12
(B) 13
(C) 15
(D) 18
(E) 19

_________________
Senior Manager
Joined: 18 May 2019
Posts: 357
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 00:12
Let points for a successful high jump be x and y be the points for a successful long jump.
Then for team A: 20=10x+5y ..........(1)
team B: 10=8x+2y equivalent to 5=4x+y ...(2)
(3)-(1) leads to 5=10x hence x=0.5
And we can get y = 3 when x=0.5 is substituted into (2)
The points gotten by Team C = 5*3 =15, since they were only successful in completing all five high jumps.

Posted from my mobile device
Senior Manager
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 00:40
1
10 long jumps and 5 high jumps .....total 15 jumps
Let x be long jump and y be high jump

Team A completed all 15 jumps, receiving 20 points. => 10x+5y=20.............eq 1

Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. => 8x+2y=10.............eq 2

Team C missed 2 long jumps and successfully completed all the high jumps.=> 8x+5y=?

Solving eq 1 & 2 for x and y gives x=0.5 and y=3

Team C's points= 8(0.5)+5(3)= 4+15 =19...........Option E
_________________

ALL ABOUT GMAT- $$https://exampal.com/gmat/blog/gmat-score-explained$$
Manager
Joined: 17 Jan 2019
Posts: 92
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 01:47
1
A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?
10L+5H=20
8L+2H=10
8L+5H=?
solve by substitution we get
L=1/2
H=3
therefore, 8(1/2)+5(3)=19
E
Manager
Joined: 05 Aug 2018
Posts: 58
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 02:04
1
Let's x be points earned from each long jump, and y be points earned from each high jump.

Team A: completed all 15 jumps and receiving 20 points -- 10x + 5y = 20 (Equation 1)
Team B: completed 8 long jumps, 2 high jumps -- 8x + 2y = 10 (Equation 2)

Solve the equation: x = 0.5, y = 3

Finding Team C points: completed 8 long jumps, 5 high jumps -- 8x + 5y = 8(0.5) + 5(3) = 19 points. -> Answer E
Senior Manager
Joined: 07 Mar 2019
Posts: 323
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 03:31
Total number of jumps in competition = 10 + 5 = 15 where n(L) = 10 and n(H) = 5.

To find = Total points of Team C.

Given that there are three teams – Team A, Team B and Team C. Let L and H be the points per jumps or Long jumps and High jumps respectively.

Team A: $$n(L) = 10$$ & $$n(H) = 5$$ and Points = 20
 $$10L + 5H = 20$$
 $$2L + H = 4$$ Eqn. ①

Team B: $$n(L) = 8$$ & $$n(H) = 2$$ and Points = 10
 $$8L + 2H = 10$$
 $$4L + H = 5$$ Eqn. ②

Team C: $$n(L) = 8$$ & $$n(H) = 5$$ and Points = ?
 Points = $$8L + 5H$$

Since we have two variables and two equations we can solve for the variables.

$$Eqn. ② - Eqn. gives 4L - 2L + H – H = 5 – 4$$
 $$2L = 1$$
 $$L = ½$$

Solving for H either equation gives $$H = 3$$

Thus, $$8L + 5H = 8 * \frac{1}{2} + 5 * 3$$
 $$8L + 5H = 19$$

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Director
Joined: 24 Nov 2016
Posts: 598
Location: United States
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 03:40
Quote:
A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?

(A) 12
(B) 13
(C) 15
(D) 18
(E) 19

[Q] 8x+5y=?
[1] 10x+5y=20
[2] 8x+2y=10
[3:1-2] 2x+3y=10
[3-2] 6x-y=0…6x=y
[2] 8x+2y=10…8x+2(6x)=10…20x=10…x=0.5
[Q] 8x+5y=…8x+5(6x)=…38x=…38(0.5)=19

Senior Manager
Joined: 10 Aug 2018
Posts: 335
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 06:34
IMO it's E, 19
We can make two equations by the question stem:
10L+5H=20
8L+2H=10
Solving these 2 we will get, H=3, L=0.5
Team C completed 8L and 5H which will total make 4+15=19 points.

A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?

(A) 12
(B) 13
(C) 15
(D) 18
(E) 19
_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL"

GMAT:[640 Q44, V34, IR4, AWA5]

GMAT Tutor
Joined: 17 Sep 2014
Posts: 198
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

Updated on: 08 Sep 2019, 01:02
We have two equations and two variables, looking to solve for the 2 variables. The first equation is $$10L + 5H = 20$$, second equation is $$8L + 2H = 10$$. We can multiply the second equation by 2.5 so that we can eliminate the variable $$H$$, this gives $$10L = 5$$ and $$L = 0.5$$, thus $$H = 3$$. The answer is $$8L + 5H = 4 + 15 = 19$$, E.
It would be good practice to try solving this in your head, the key here is to find a nice variable to eliminate and here we multiply the second equation by 2.5 to match the $$5H$$ in the first equation.
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!

Originally posted by TestPrepUnlimited on 03 Sep 2019, 07:44.
Last edited by TestPrepUnlimited on 08 Sep 2019, 01:02, edited 1 time in total.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5014
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

### Show Tags

03 Sep 2019, 22:46
given
h+l=15
h=10 and l=5
also
10x+5y=20
8x+2y=10
find
8x+5y
solve for x& y ; x= 0.5 and y=3
so 8x+5y= 19
IMO E

A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?

(A) 12
(B) 13
(C) 15
(D) 18
(E) 19
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps   [#permalink] 03 Sep 2019, 22:46
Display posts from previous: Sort by