SatsMunchers 1 Answers Special Numbers & Sequences

Q1.  Which multiple of 7 lies between 30 and 40? A1.  35      There's loads of multiples of 7:  7, 14, 21, 28, 35, 42 . .. but only 35 lies between 30 and 40! Q2.  Which factor of 24 lies between 10 and 20? A2.  12      24 can be made from:  1 x 24,  2 x 12,  3 x 8,  4 x 6 So, 24 has 8 factors:    1, 2, 3, 4, 6, 8, 12, 24 ... but only 12 fits the question.   Q3.  What's the square of 8? A3.  64      The 'square of 8' means '8 times itself' or '8 x 8'

Q4.  Can you complete this sequence:           13,  9,  5,  1, __ ,  __ ? A4.  -3 and -7          The sequence is going down (or decreasing) by 4 each time. Q5. Can you complete this sequence:             3, __ ,  15,  21,  27 ? A5.  9          The sequence is going up (or increasing) by 6 each time. Q6.  The first four numbers of a sequence are:         11, 15, 19, 23 ... Which description fits this sequence: A.  The first number is 4 and the sequence increases by 11 each time? B.  The first number is 11 and the sequence  increases by 5 each time? C.  The first number is 11 and the sequence decreases by 4 each time? D.  The first number is 11 and the sequence increases by 4 each time? A6.  D          Did you choose one of the other three choices?   They were VERY similar - try to read questions more slowly. Q7.  I'm thinking of a number -        Clue 1: It is less than 30.        Clue 2: It is both a multiple of 6 and 9       What number am I thinking of ? A7.  18:          18 is a multiple of both 6 and 9 - so it's a 'common multiple': 1st few Multiples of 6: 6, 12, 18, 24, 30, 36, 42 ... Ist few Multiples of 9: 9, 18, 27, 36, 45, 54, 63 ... You can see that 6 and 9 have both 18 and 36 in common (And that 18 is the LOWEST common multiple) Q8.  2 and 24 are a factor pair of 48.        Which is the correct list for the remaining factor pairs?        A.  3 and 16,      4 and 12        B.  3 and 16,      4 and 12,      6 and 7        C.  1 and 48,      3 and 16,      4 and 12,      6 and 8        D.  3 and 16,      4 and 12,      6 and 8 A8.  C A misses out 1 x 24 (the most common mistake) B misses these AND 6 x 8 D misses out LOADS It's just too easy to miss out just one factor ... So, it's safer to work them out in order, starting with 1, then 2, then 3 ... 1 X 48   2 X 24   3 X 16   4 X 16   6 X 8   (8 X 6 is a repeat so you know to stop).

Q9.  The nth term of a sequence is n(n + 2).           What is the 4th term of this sequence? A9.  24 First, think of n as the position number.  For example, in the sequence: 1, 4, 7, 10 ... 7 is the 3rd position number. So, when n = 3, the nth term is 7 Now turn the question into plain English: 'nth term = n(n + 2) '   becomes ... ' any term in this sequence will always equal the position number multiplied by 2 more than the position number ' (OK, so it's long - but it does make sense if you read it enough times!) So The 4th number = n x (n + 2)                              = 4 x (4 + 2)                              = 4 x 6                             = 24 (If you wanted to know which sequence it is, then: 1st term  = 1 x 3 = 3 2nd term = 2 x 4 = 8 3rd term  = 3 x 5 = 15 4th term  = 4 x 6 = 24 So, sequence is:  3, 8, 15, 24) Q10.  A sequence starts with 1, 4, 7, 10 ...          What is the nth term of this sequence?  A10.  3n-2 The clue here is that the sequence goes up in threes - just like the 3 times tables.  The only question them is 'how far  awayis the 3 times tables from this sequence? - Position Number:     1st    2nd    3rd    4th x3:               3        6       9      12     try subtracting 2? -2:                1        4       7       10     correct Using words:      'Any term is 3 times the position number and subtract 2' Using maths:  nth term = 3 x n - 2  or  3n - 2