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09 May 2019, 21:27
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
22% (02:59) correct
78%
(02:54)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
How many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line \(y=\pi x\), the line y = -0.1 and the line x = 5.1?
(A) 30
(B) 41
(C) 45
(D) 50
(E) 57
(A) 30
(B) 41
(C) 45
(D) 50
(E) 57
14 May 2019, 03:15
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When x=0, no integral value of y lie in region
When x=1, 0=<y<3.14 Hence 4 points lie in region
When x=2, 0=<y<6.28 Hence 7 points lie in region
When x=3, 0=<y<9.42 Hence 10 points lie in region
When x=4, 0=<y<12.56 Hence 13 points lie in region
When x=5, 0=<y<15.70 Hence 16 points lie in region
First count Total squares with side 1*1
When we choose 2 points on x=1 and 2 points on x=2, squares possible= 4-1=3
When we choose 2 points on x=2 and 2 points on x=3, squares possible= 7-1=6
When we choose 2 points on x=3 and 2 points on x=4, squares possible= 10-1=9
When we choose 2 points on x=4 and 2 points on x=5, squares possible= 13-1=12
Hence total 1*1 squares= 12+9+6+3+0=30
count Total squares with side 2*2=
When we choose 2 points on x=1 and 2 points on x=3, squares possible=4-2=2
When we choose 2 points on x=2 and 2 points on x=4, squares possible=7-2=5
When we choose 2 points on x=3 and 2 points on x=5, squares possible=10-2=8
Hence total 2*2 squares= 2+5+8=15
count Total squares with side 3*3=
When we choose 2 points on x=1 and 2 points on x=4, squares possible=4-3=1
When we choose 2 points on x=2 and 2 points on x=5, squares possible=7-3=4
Hence total 3*3 squares= 1+4=5
There are 0 4*4 squares possible
Total squares lie in the region= 30+15+5=50
When x=1, 0=<y<3.14 Hence 4 points lie in region
When x=2, 0=<y<6.28 Hence 7 points lie in region
When x=3, 0=<y<9.42 Hence 10 points lie in region
When x=4, 0=<y<12.56 Hence 13 points lie in region
When x=5, 0=<y<15.70 Hence 16 points lie in region
First count Total squares with side 1*1
When we choose 2 points on x=1 and 2 points on x=2, squares possible= 4-1=3
When we choose 2 points on x=2 and 2 points on x=3, squares possible= 7-1=6
When we choose 2 points on x=3 and 2 points on x=4, squares possible= 10-1=9
When we choose 2 points on x=4 and 2 points on x=5, squares possible= 13-1=12
Hence total 1*1 squares= 12+9+6+3+0=30
count Total squares with side 2*2=
When we choose 2 points on x=1 and 2 points on x=3, squares possible=4-2=2
When we choose 2 points on x=2 and 2 points on x=4, squares possible=7-2=5
When we choose 2 points on x=3 and 2 points on x=5, squares possible=10-2=8
Hence total 2*2 squares= 2+5+8=15
count Total squares with side 3*3=
When we choose 2 points on x=1 and 2 points on x=4, squares possible=4-3=1
When we choose 2 points on x=2 and 2 points on x=5, squares possible=7-3=4
Hence total 3*3 squares= 1+4=5
There are 0 4*4 squares possible
Total squares lie in the region= 30+15+5=50
Bunuel
17 May 2019, 06:48
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Is it really possible to get such lengthy questions in GMAT?
