11 Plus Exams Forum

I am struggling with the answer(!) and the easiest method to tackle questions like this:

Brian starts with 1000 and subtracts 11 each time. The first 4 numbers in his sequence are: 1000 , 989 , 978 , 967
If he continues in this way, what will be the first negative number in his sequence?


It came from a past paper from an independent school and I am just wondering what "topic" it comes under. Also, does anyone know of other similar examples we could practise?

Grateful for any help and advice!

I make it -8

not sure if it's right though, I continued to subtract 11 (although in bunches of 10x11= 110) until I got down to 80,

8x11 =88

so we are 8 below 0 =-8




ignore that, I took 111 away instead of 110 , not concentrating..just what i moan at pupils for
should be

1000-110
890
780
670
560
450
340
230
120
10

10 -11 =-1

Doh!

Off the top of my head

You could sit and subtract 11 until you get bored

A quicker way would be long division dividing by 11 and looking at the remainder, 990 plus 10, so from 10 take away 11 leaves -1.

You could use a table to estimate the number of whole 11s in 1000,


11s___Total

100____1100 too many
80_____880 too few
90____990 plus ten makes 1000

Don't have any more examples to hand, it is a test of having a "feel" for numbers and working out a solution to a problem.

Hopefully a maths expert will be along shortly???

steve

Steve is correct

Essentially what they need to work out is an equality such that

1000 - 11n < 0

where n is a whole Integer

So divide 1001, 1002 etc by eleven until you get the first whole integer
(if they divide 1000 by 11 you can see that you get 90 remainder 10 so 1001 must be the 1st whole number)

You can see that 1001 is the 1st number and n = 91

hence the anser is -1

that is complicated!
I am hoping that this sort of question is one of the stinkers they put in to sort out the maths whizzes from the rest because I don't think I can explain it simply enough to my son.

Sorry, forgot to say thank you for all of your help!