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05 May 2020, 03:15
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C
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Difficulty:
95%
(hard)
Question Stats:
40% (02:45) correct
60%
(02:56)
wrong
based on 125
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How many pairs positive integers x and y satisfy 2x + y < 40, if y is a multiple of x?
A. 90
B. 91
C. 92
D. 93
E. 94
Are You Up For the Challenge: 700 Level Questions
A. 90
B. 91
C. 92
D. 93
E. 94
Are You Up For the Challenge: 700 Level Questions
05 May 2020, 05:32
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Bunuel
So y = ax where a= 1, 2, 3....
We will now calculate for each value of ax..
1) \(a=1...2x + x < 40....3x<39+1....x<13+\frac{1}{3}.......1\leq{x}\leq{13}....13\) values
2) \(a=2...2x + 2x < 40....4x<40....x<10.......1\leq{x}<{10}....9\) values
3) \(a=3...2x + 3x < 40....5x<40....x<8.......1\leq{x}<8....7\) values
4) \(a=4...2x + 4x < 40....6x<36+4....x<6+\frac{4}{6}.......1\leq{x}\leq{6}....6\) values
5) \(a=5...2x + 5x < 40....7x<35+5....x<5+\frac{5}{7}.......1\leq{x}\leq{5}....5\) values
6) Now 40/8 and 40/9 are between 4 and 5, so when a=6 and a=7, we will get x as 1 to 4, so 2*4=8 values
7) Now 40/10 to 40/13 are between 3 and 4, so when a=8 to 11, we will get x as 1 to 3, so 4*3=12 values
8) Now 40/14 and 40/19 are between 2 and 3, so when a=12 to 17, we will get x as 1 and 2, so 6*2=12 values
9) Now 40/20 to 40/39 are between 1 and 2, so when a=18 to 37, we will get x as 1, so 20*1=20 values..
Total = 13+9+7+6+5+8+12+12+20=92
C
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 820
06 May 2020, 01:39
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Bunuel
2x + y < 40 and y is a multiple of x.
1) When x = 1 => y< 38 => 37 values
2) When x = 2, y < 36 => 17 values (only multiples of 2)
3) When x = 3, y < 34 => 11 values (only multiples of 3)
4) When x = 4, y < 32 => 7 values (only multiples of 4)
5) When x = 5, y < 30 => 5 values (only multiples of 5)
6) When x = 6, y < 28 => 4 values (only multiples of 6)
7) When x = 7, y < 26 => 3 values (only multiples of 7)
8) When x = 8, y < 24 => 2 values (only multiples of 8)
9) When x = 9, y < 22 => 2 values (only multiples of 9)
10) When x = 10, y < 20 => 1 values (only multiples of 10)
11) When x = 11, y < 18 => 1 values (only multiples of 11)
12) When x = 12, y < 16 => 1 values (only multiples of 12)
13) When x = 13, y < 14 => 1 value (only 13)
13) When x = 14, y < 12 => 0 values
Total = 37+17+11+7+5+4+3+2+2+1+1+1+1 = 92
Answer - C
