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If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 02:59
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Competition Mode Question If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are there? A. 6 B. 5 C. 4 D. 3 E. 2
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 03:15
IMO B,
3x+4y=33 (equation)
Putting X = 1, Y = 30/4 =7.5(not integer)
Putting X = 2, Y = 27/4 =6.75(not integer)
Putting X = 3, Y = 24/4 =6(integer) Therefore y = +6 (1)
Putting X = 4, Y = 21/4 =5.25(not integer)
Putting X = 5, Y = 18/4 =4.5(not integer)
Putting X = 6, Y = 15/4 =3.75(not integer)
Putting X = 7, Y = 12/4 =3(integer) Therefore Y = +3 (2)
Putting X = 8, Y = 9/4 =2.25(not integer)
Putting X = 9, Y = 6/4 =1.5(not integer)
Putting X = 10, Y = 3/4 =0.75(not integer)
Putting X = 11, Y = 0/4 =0(integer) Therefore Y = 0 (3)
Total values of y = 6,+6,3,+3,0 (5 values)
Answer should be B
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 03:17
If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are there?
A. 6 B. 5 C. 4 D. 3 E. 2
Given: x > 0 \(y = \frac{3(11x)}{4}\)
possible values of x,y: [(3,6),(7,3),(11,0)] we can not go any further as mod can not be less than 0 Ans: D



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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 03:27
D. Given: x > 0 and 3x + 4y = 33; Simplifying the eqn for y; y = 3(11x)/4 Since it given that y is +ve and it is not mentioned that y>0, three values of x satisfies the equation: (3,6), (7,3), (11, 0)
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 03:34
\(3x + 4y = 33\)
\(y=\frac{333x}{4}=\frac{3(11x)}{4}\)
\((11x)\) is a multiple of \(4\)
So \(x\) can be \(3, 7 or 11\)
When \(x=3\) or \(7\), \(y\) can take two values (+ve/ve) for each and when \(x=11,y=0\)
(x,y)=(3,6) (3,6) (7,3) (7,3) (11,0)
Answer is (B)
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 04:16
to get an odd answer which is 33, we must add an odd number with an even number and we can get odd number in only multiples of 3 as we can only get even numbers in multiples of 4. We should try with every odd multiples of 3 to add with multiples of 4
Pairs  21+12 & 24+9
Answer  E



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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 06:01
x > 0; x and y are both integers.
3x + 4y = 33 > y = 3(11x)/4 (11x) has to be a multiple of 4, thus x = 11,7,3
For x=11... y=0 For x=7... y=1 or y=1 For x=3... y=2 or y=2 Obviously, there are 5 integer pairs (x, y)
FINAL ANSWER IS (B)
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 06:44
Quote: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are there?
A. 6 B. 5 C. 4 D. 3 E. 2 x>0, then x=(334y)/3>0 and an integer (334y)/3>0, 334y>0, 4y<33, y<33/4, 33/4<y<33/4, 8≤y≤8 x=114/3y>0 and an integer 8≤y=multiple of 3≤8 y={6,3,0,3,6}=5 y=6: x=114/3*6=11+8=19 y=6: x=114/3*6=118=3 both are in range (x,y) pairs are 5 Ans (B)



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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 07:14
Given x>0, x and you are integers. 3X+4y=33 y is integer if x=3 , 7 or 11 So possible ordered pair (x, y) are (3, 6), (3, 6), (7, 3) (7, 3) &(11,0)i.e total 5 pairs. So correct ans is (B).
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 08:18
IMO B
If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are there?
x = 11  4/3y >0 y < 33/4 =8.25 & for integral values, y multiple of 3, So, possible values are y = { 0, 3, 6 } y = { 6, 3, 0, 3 , 6} So total 5 pairs of (x,y)
B. 5



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If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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Updated on: 29 May 2020, 03:33
given relation of x > 0 and 3x + 4y = 33 would be valid at y=+/7 ; x= 2 y=+/6 ; x=3 y=0 ; x= 11 total pairs ; 5 possible OPTION B
If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are there?
A. 6 B. 5 C. 4 D. 3 E. 2
Originally posted by Archit3110 on 28 May 2020, 10:16.
Last edited by Archit3110 on 29 May 2020, 03:33, edited 1 time in total.



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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 15:23
Is it B ? If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are there? X > 0 . so 3x + 4y = 33 => y = 3/4 (11x) .. X can be 3 , 7 , 11 and y can be 6 , 3 , 0 respectively . However as per ques with ve value of y also the equation will be satisfied . So total 5 pair of x and y will satisfy the equation.. (3,6) , (3,6) ,(7,3) , (7,3) and (11,0) Hence B , IMO .
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Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 22:06
Ans:C 3x + 4y = 33 3x+4y=33..y=(333x)/4 as x>0 x=3 y=6 x=7 y=3
3x4y=33 y=(3x33)/4 x=3 y=6 x=7 y=3 x=15 y=3..no possible as 3*15=45 so total 4 pairs




Re: If x > 0 and 3x + 4y = 33, then how many integer pairs of (x, y) are
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28 May 2020, 22:06




