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y=\frac{3 x}{4}+9 , where y
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19 Aug 2026, 04:38
19 Aug 2026, 04:38
Expert Reply
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Question Stats:
22% (03:03) correct
77% (02:04) wrong based on 9 sessions
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\( y=\frac{3 x}{4}+9\) , where y is an integer and \(0<\mathrm{x}<20\) .
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The number of different possible values of y |
14 |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
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Re: y=\frac{3 x}{4}+9 , where y
[#permalink]
19 Aug 2026, 16:47
19 Aug 2026, 16:47
Expert Reply
1. Given Information
\(y=\frac{3 x}{4}+9\)
y must be an integer.
\(0<x<20\) (note that $x$ is not restricted to integers; x can be any real number within this range).
2. Range of y
Substitute the bounds of $x$ into the equation to find the range of possible values for y :
Lower bound for $y$ (as $x \rightarrow 0$ ):
\(y>\frac{3(0)}{4}+9=9\)
Upper bound for $y$ (as \(x \rightarrow 20\) ):
\(y<\frac{3(20)}{4}+9=15+9=24\)
Combining these bounds gives:
\(9<y<24\)
3. Integer Values for y
Since x can be any real number in the open interval (0,20) , the term \(\frac{3 x}{4}\) continuously takes every real value between 0 and 15.
Consequently, y can take every integer value strictly between 9 and 24 :
\(y \in\{10,11,12,13,14,15,16,17,18,19,20,21,22,23\}\)
To count the total number of integer values in this set:
\(\text { Count }=23-10+1=14\)
4. Comparing Quantities
Quantity A: The number of different possible values of y=14
Quantity B: 14
Both quantities are equal.
\(y=\frac{3 x}{4}+9\)
y must be an integer.
\(0<x<20\) (note that $x$ is not restricted to integers; x can be any real number within this range).
2. Range of y
Substitute the bounds of $x$ into the equation to find the range of possible values for y :
Lower bound for $y$ (as $x \rightarrow 0$ ):
\(y>\frac{3(0)}{4}+9=9\)
Upper bound for $y$ (as \(x \rightarrow 20\) ):
\(y<\frac{3(20)}{4}+9=15+9=24\)
Combining these bounds gives:
\(9<y<24\)
3. Integer Values for y
Since x can be any real number in the open interval (0,20) , the term \(\frac{3 x}{4}\) continuously takes every real value between 0 and 15.
Consequently, y can take every integer value strictly between 9 and 24 :
\(y \in\{10,11,12,13,14,15,16,17,18,19,20,21,22,23\}\)
To count the total number of integer values in this set:
\(\text { Count }=23-10+1=14\)
4. Comparing Quantities
Quantity A: The number of different possible values of y=14
Quantity B: 14
Both quantities are equal.
gmatclubot
Re: y=\frac{3 x}{4}+9 , where y [#permalink]
19 Aug 2026, 16:47
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