[PDF] Australian Mathematics Competition AMC Warm-Up Paper 7 Upper Primary Solutions.pdf | Plain Text

AMC WARM-UP PAPER UPPER PRIMARY 7 SOLUTIONS c 2009 Australian Mathematics Trust 1.2694÷100 = 26.94, hence (B). 2.You buy 30 litres and save 4 c per litre, so you save 30×4c= 120 c = $1.20, hence (D). 3.The difference between 2 below zero and 10 above is 12 degrees Celsius, hence (E). 4.Sally’s post-it notes are half the size of Henry’s, so it would take twice as many, 2×100 = 200, of her post-it notes to cover Henry’s desk, Since her desk is twice the size of Henry’s it will take twice that number, 2×200 = 400, of her post-it notes to cover her desk, hence (E). 5.If we consider the different ways we can travel if we keep moving to the right, we can get the five waysPQT,PRST,PRQT,PQSTandPRQST. • P • R• Q • S• T ..................................................................................................... ........................................................................... ............. ...... ..... .. .. ... .... ... .. ... ... .. .. .. ... .. . .. .. .. .. . .. .. . .. . .. . .. . .. . . .. . . .. . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................ ..................................................................................................... ............................................................... ................. ......... ....... ..... . ..... .... ..... .... .... ... .... ... ... ... ... ... ... ... .. ... .. ... .. ... .. .. ... .. .. .. .. .. ... .. .. .. .. . .. .. .. .. .. .. . .. .. .. . .. .. .. . .. .. . .. . .. .. . .. . .. . .. . .. .. . . .. . .. . .. . .. . . .. . .. . . .. . .. . . .. . . .. . . .. . . . .. . . .. . . . .. . . . .. . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. . . . .. . . . . . . . .. . .. . . .. .. . .. . .. .. . .. .. .. .. .. .. .. .. ... .. ... ... ... ... .... .... ..... ...... .............. ............ ..................................................................................................... ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . .. . . . .. . . . .. . . .. . .. . . .. . .. . .. . .. .. . .. .. . .. .. .. . . .. .. .. .. .. .. ... .. .. ... ... .. ... ... .... ... .... .... ..... ..... ....... .......... ......................... ..................................................................................................... ..................................................................................................... ............................................................ . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . .. . . . . .. . . .. . . .. . . .. . .. . .. . .. . .. . .. .. . .. .. .. . .. .. .. .. .. .. ... .. .. ... .. ... ... .... ... ... .... .... ..... ...... . ..... .. . .... .. ... .. .. .. ... .... ..... ...... ...................................................................... ..................................................................................................... ............. In addition to these 5 routes, we can also travelPQRSTandPRSQT,sothere are 7 ways, hence (D).

UP7 Solutions Page 2 6.Fred and Anne together weigh 62 kg and Fred and Sally together weigh 59 kg. This means that Anne weighs 3 kg more than Sally. Now, since Sally and Anne together weigh 53 kg, if we take 3 kg from the 53 kg, this must be twice Sally’s weight, so Sally weighs 50÷2=25kg, hence (A). 7.Since the statements imply that there is at least one green, one blue and one red crayon, for each of the statements all of them are green except two, all of them are blue except two, all of them are red except two, to be true, there must be no more then 3 pens, one of each colour, otherwise at least one of the above statements would be false. So Mel has three crayons, hence (A). 8.Since 770 = 10×77 = 2×5×7×11, the only numbers we can choose to multiply from this set to give a possible age for a teenager is 2×7 = 14, so Gina’s teenager must be 14, hence (B). 9.Since Phil sits at a desk fourth from the front and third from the back, there must be 6 rows of desks. Since there are four desks to the right of Phil’s and one to the left, there must be 6 columns of desks. There are then 6 rows and 6 columns of desks in the classroom, which is 6×6=36 desks.

UP7 Solutions Page 3 10.Consider the 6 by 6 block as shown. All the outside apartments have exterior views, so we need only deal with the 16 interior squares. figure 1 Putting in one garden will remove one apartment and bring light to (at most) four other apartments. G This complying arrangement will deal with at most five of the internal squares and so, as 3×5