It is currently Thu Jan 18, 2018 9:48 pm

 All times are UTC

 Page 1 of 1 [ 10 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 6:25 am

Joined: Fri Oct 30, 2009 11:08 pm
Posts: 1234
Do not panic anyone this is not an 11 plus question.

DS has this for homework. We have eventually by trial and error got what we think is the right answer but can anyone explain how we should have mathematically worked it out.

Amrita has written down four whole numbers. If she chooses three of her numbers at a time and adds up each triple, she obtains totals of 115, 153, 169 and 181.

What is the largest of Amrita's numbers?

A 66
B 53
C 91
D 121
E 72

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 6:29 am

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7138
Location: East Kent
I would tend to work down from the 121 and eliminate.
can't be 121 as there are no others small enough to make 181

So trial and error really. Sorry not much help!

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 9:32 am

Joined: Sat Sep 27, 2008 9:51 pm
Posts: 2337
This is how I did it - but it seems a bit convoluted, there may be a quicker way:

Calling the numbers a, b, c, d in ascending order,

(1) a + b + c = 115
(2) a + b + d = 153
(3) a + c + d = 169
(4) b + c + d = 181

subtract (1) from (4)
d - a = 181 - 115 = 66
a = d + 66

If d = 121, a = 55 and b + c = 60:
a + d = 176 so (b + c = 60) doesn't work because b and c would both have to be negative for eqns (2) and (3) to work out

If d = 91, a = 25 and b + c = 90:
a + d = 116
b = 153 - 116 = 37
c = 169 - 116 = 53
53 + 37 = 90 so that works.

Takes a long time tho', and since they're looking for people with a natural flair for maths the official solution may have something more brisk and not very intuitive to the rest of us.

Mike

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 10:30 am

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1330
Location: Watford, Herts
Minesatea wrote:
Amrita has written down four whole numbers. If she chooses three of her numbers at a time and adds up each triple, she obtains totals of 115, 153, 169 and 181.

What is the largest of Amrita's numbers?

Each of the original numbers occurs in three of the totals, so the total of the four numbers is (115+153+169+181)/3 = 206, and thus the largest number was 206 - 115 = 91.

Checking the answer (always a good idea): similarly the other numbers are

206 - 153 = 53
206 - 169 = 37
206 - 181 = 25

and we can reconstruct the totals

25 + 37 + 53 = 115
25 + 37 + 91 = 153
25 + 53 + 91 = 169
37 + 53 + 91 = 181

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 10:44 am

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1330
Location: Watford, Herts
A simpler variant from the 1988 challenge:
Quote:
Weighing the baby at the clinic was a problem. The baby would not keep still and caused the scales to wobble. So I held the baby and stood on the scales while the nurse read off 78 kg. Then the nurse held the baby while I read off 69 kg. Finally I held the nurse while the baby read off 137 kg. What was the combined weight of all three (in kg)?

A 142 B 147 C 206 D 215 E 284

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 11:48 am

Joined: Fri Oct 30, 2009 11:08 pm
Posts: 1234
Thanks WP. That was the answer he got but it took 20 mins so I was sure there had to be a simple way!

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Wed Apr 27, 2011 11:51 am

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7138
Location: East Kent
I reckon for a junior maths challenge they are looking for someone to think around the problem, rather than just applying a learnt formula.

That's my excuse anyway

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Sun May 29, 2011 7:00 pm

Joined: Thu May 26, 2011 8:37 pm
Posts: 577
Are these questions typical of 11+ (I know the OP's question wasn't, but the rest?) They are beyond me.

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Tue May 31, 2011 1:53 pm

Joined: Wed Feb 27, 2008 8:59 am
Posts: 2078
menagerie wrote:
Are these questions typical of 11+ (I know the OP's question wasn't, but the rest?) They are beyond me.

JMC questions are aimed at the top third, of year 8 children.
http://www.mathcomp.leeds.ac.uk/individ ... challenge/

Top

 Post subject: Re: Junior Maths challenge question helpPosted: Tue May 31, 2011 5:57 pm

Joined: Thu May 26, 2011 8:37 pm
Posts: 577
Thanks Mitasol. That's some comfort. I'm sure my husband could do them, but not convinced he could explain how to our sons...

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 10 posts ]

 All times are UTC

#### Who is online

Users browsing this forum: No registered users and 3 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ FORUM RULES    Forum Rules and FAQs 11 PLUS SUBJECTS    VERBAL REASONING    MATHS    ENGLISH    NON-VERBAL REASONING    CEM 11 Plus GENERAL    GENERAL 11 PLUS TOPICS    11 PLUS APPEALS    11 PLUS TUTORS    INDEPENDENT SCHOOLS    11 PLUS CDs/SOFTWARE    11 PLUS TIPS    PRIMARY    SEN and the 11 PLUS    EVERYTHING ELSE .... 11 PLUS REGIONS    Berkshire    Bexley and Bromley    Birmingham, Walsall, Wolverhampton and Wrekin    Buckinghamshire    Devon    Dorset    Essex    Essex - Redbridge    Gloucestershire    Hertfordshire (South West)    Hertfordshire (Other and North London)    Kent    Lancashire & Cumbria    Lincolnshire    Medway    Northern Ireland    Surrey (Sutton, Kingston and Wandsworth)    Trafford    Warwickshire    Wiltshire    Wirral    Yorkshire BEYOND 11 PLUS    Beyond 11 Plus - General    GCSEs    6th Form    University