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Recent questions tagged algebra
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 59
Each of $a, b, c$, and $d$ is a positive integer and is greater than $3.$ If $ \frac{1}{a-2}=\frac{1}{b+2}=\frac{1}{c+1}=\frac{1}{d-3} $ then which ordering of these four numbers is correct? $a\lt b\lt c\lt d$ $c\lt b\lt a\lt d$ $b\lt a\lt c\lt d$ $b\lt c\lt a\lt d$
Each of $a, b, c$, and $d$ is a positive integer and is greater than $3.$ If$$\frac{1}{a-2}=\frac{1}{b+2}=\frac{1}{c+1}=\frac{1}{d-3}$$then which ordering of these four n...
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 62
In the sum shown, $P, Q$ and $R$ represent three different single digits. The value of $P+Q+R$ is ______. $ \begin{array}{ccc} & P \;7 \;R \\ + & 3\;9\; R \\ \hline & R\; Q\; 0 \end{array}$ $13$ $12$ $14$ $3$
In the sum shown, $P, Q$ and $R$ represent three different single digits. The value of $P+Q+R$ is ______.$$\begin{array}{ccc}& P \;7 \;R \\+ & 3\;9\; R \\\hline & R\; Q\;...
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Jan 19
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11
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2
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3
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 63
A town has $2017$ houses. Of these $2017$ houses, $1820$ have a dog, $1651$ have a cat, and $1182$ have a turtle. If $x$ is the largest possible number of houses that have a dog, a cat, and a turtle, and $y$ is the smallest possible number of houses that have a dog, a cat, and a turtle, then $x-y$ is ______. $1182$ $638$ $563$ $619$
A town has $2017$ houses. Of these $2017$ houses, $1820$ have a dog, $1651$ have a cat, and $1182$ have a turtle. If $x$ is the largest possible number of houses that hav...
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Jan 19
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6
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4
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 64
The integers $1,2,4,5,6,9,10,11,13$ are to be placed in the circles and squares below with one number in each shape. Each integer must be used exactly once and the integer in each circle must be equal to the sum of the integers in ... $x+y?$ $19$ $20$ $21$ $24$
The integers $1,2,4,5,6,9,10,11,13$ are to be placed in the circles and squares below with one number in each shape.Each integer must be used exactly once and the integer...
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Jan 19
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4
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5
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 9
If $a, b$, and $c$ are real numbers, which of the following are necessarily true? If $a<b$ and $a b \neq 0$, then $\frac{1}{a}>\frac{1}{b}$ If $a<b$, then $a c<b c$ for all $c$ If $a<b$, then $a+c<b+c$ for all $c$. If $a<b$. then $-a>-b$ I only I and III only III and IV only I, III, and IV only
If $a, b$, and $c$ are real numbers, which of the following are necessarily true?If $a<b$ and $a b \neq 0$, then $\frac{1}{a}>\frac{1}{b}$If $a<b$, then $a c<b c$ for all...
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Jan 13
Quantitative Aptitude
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6
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6
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 10
Let $n$ be any positive integer and $1 \leq x_1<x_2<\ldots<x_{n+1} \leq 2 n$, where each $x_i$ is an integer Which of the following must be true? There is an $x_i$ that is the square of an integer. There is an $i$ such that $x_{i+1}=x_i+1$. There is an $x_i$ that is prime I only II only I and II I and III
Let $n$ be any positive integer and $1 \leq x_1<x_2<\ldots<x_{n+1} \leq 2 n$, where each $x_i$ is an integer Which of the following must be true?There is an $x_i$ that is...
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Jan 13
Quantitative Aptitude
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7
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 1
Consider the following statements: $\text{S1}:$ Suppose $a, b, c \in \mathbb{Z}$. If $a^2 \mid b$ and $b^3 \mid c,$ then $a^6 \mid c$. $\text{S2}:$ Suppose $a \in \mathbb{Z}$. If $a^3$ ... of the above statements is true? Only $\text{S1}$. Only $\text{S2}$. Both $\text{S1} \;\& \;\text{S2}$. None
Consider the following statements:$\text{S1}:$ Suppose $a, b, c \in \mathbb{Z}$. If $a^2 \mid b$ and $b^3 \mid c,$ then $a^6 \mid c$.$\text{S2}:$ Suppose $a \in \mathbb{Z...
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
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algebra
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3
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2
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8
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 2
Consider the following statements: $\text{S1}:$ If $a, b \in Z$ and $a+b$ is even, then $a^ 2+b^ 2$ is even. $\text{S2}:$ If $a, b \in Z$ and $a+b$ is odd, then $a^ 2+b^ 2$ is odd. Which of the above statements is true? Only $\text{S1}$ Only $\text{S2}$ Both $\text{S1}\; \&\; \text{S2}$ None
Consider the following statements:$\text{S1}:$ If $a, b \in Z$ and $a+b$ is even, then $a^ 2+b^ 2$ is even.$\text{S2}:$ If $a, b \in Z$ and $a+b$ is odd, then $a^ 2+b^ 2$...
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
goclasses
quantitative-aptitude
algebra
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2
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9
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 3
Consider the following statements: $\text{S1}:$ Suppose $a, b \in \mathbb{Z}$. If $\left(a^ 2\right)\left(b^ 2-2 b\right)$ is odd, then both $a$ and $b$ are odd. $\text{S2}:$ Suppose $a, b \in \mathbb{Z}$. If ... Which of the above statements is true? Only $\text{S1}$ Only $\text{S2}$ Both $\text{S1}\; \&\; \text{S2}$ None
Consider the following statements:$\text{S1}:$ Suppose $a, b \in \mathbb{Z}$. If $\left(a^ 2\right)\left(b^ 2-2 b\right)$ is odd, then both $a$ and $b$ are odd.$\text{S2}...
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
goclasses
quantitative-aptitude
algebra
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2
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3
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10
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 4
Consider the following statements: $\text{S1}:$ If an integer ' $a$ ' is even then $\left(a^ 2\right)+2 a+9$ is odd. $\text{S2}:$ For an integer ' $a$ ', if $\left(a^ 2\right)+2 a+9$ is odd then ... of the above statements is true? Only $\text{S1}$ Only $\text{S2}$ Both $\text{S1}\; \&\; \text{S2}$ None
Consider the following statements:$\text{S1}:$ If an integer ' $a$ ' is even then $\left(a^ 2\right)+2 a+9$ is odd.$\text{S2}:$ For an integer ' $a$ ', if $\left(a^ 2\rig...
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Mar 8, 2023
Quantitative Aptitude
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algebra
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12
votes
1
answer
11
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 5
Consider the following statements: $\text{S1}:$ Given any $x \in \mathbb{R}$, there exists an element $y \in \mathbb{R}$ for which $x y=1$. $\text{S2}:$ There exists two irrational numbers $x$ and $y$ such that $x+y$ is ... above statements is true? Only $\text{S1}$ Only $\text{S2}$ Both $\text{S1}\; \&\; \text{S2}$ None
Consider the following statements:$\text{S1}:$ Given any $x \in \mathbb{R}$, there exists an element $y \in \mathbb{R}$ for which $x y=1$.$\text{S2}:$ There exists two ir...
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
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quantitative-aptitude
algebra
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6
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2
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12
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 6
Which of the following statements is/are True? If $x$ and $y$ are two integers whose product is odd, then both must be odd. If $a$ and $b$ ... $m^{2}$ is even, then $m$ is even. The sum of a rational number and an irrational number is irrational.
Which of the following statements is/are True?If $x$ and $y$ are two integers whose product is odd, then both must be odd.If $a$ and $b$ are real numbers such that the pr...
GO Classes
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Mar 8, 2023
Quantitative Aptitude
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quantitative-aptitude
algebra
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13
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3
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13
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 8
Let $n$ be a positive integer. Which of the following statements is/are true? If $m, a$ are positive integers and $m \mid a^ n$, then $m^ n \mid a^ n$. If $p$ is a prime and $a$ is a positive integer and $p \mid a^n$ ... odd, then $t^ n$ is also odd, for all $n$. If $t$ is even, then $t^ n$ is also even, for all $n$.
Let $n$ be a positive integer.Which of the following statements is/are true?If $m, a$ are positive integers and $m \mid a^ n$, then $m^ n \mid a^ n$.If $p$ is a prime and...
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
goclasses
quantitative-aptitude
algebra
multiple-selects
2-marks
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2
votes
1
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14
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 9
Consider the following statements: If $n \in \mathbb{Z}$, then $5 n^2+3 n+7$ is odd. If $n \in \mathbb{Z}$, then $n^2+3 n+4$ is even. Which of the above statements is true? (Hint: $n$ can be either even or odd) Only $1$ Only $2$ Both $1 \;\&\; 2$ None
Consider the following statements:If $n \in \mathbb{Z}$, then $5 n^2+3 n+7$ is odd.If $n \in \mathbb{Z}$, then $n^2+3 n+4$ is even.Which of the above statements is true?(...
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
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quantitative-aptitude
algebra
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6
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2
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15
GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 10
Two integers have the same parity if they are both even or they are both odd. Otherwise, they have opposite parity. Which of the following statements is/are true? If two integers have the same parity, their sum is odd. If two integers have opposite ... Suppose $a, b \in \mathbb{Z}$. If $a b$ is odd, then $a^2+b^2$ is even.
Two integers have the same parity if they are both even or they are both odd. Otherwise, they have opposite parity. Which of the following statements is/are true?If two i...
GO Classes
353
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Mar 8, 2023
Quantitative Aptitude
goclasses2025_csda_wq2
goclasses
quantitative-aptitude
algebra
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