Practisequestions

Practisequestions

  • FM: Practise SET-3

    Factors & Multiples: Level 3 1. When positive integer \(x\) is divided by 8, the remainder is 3. What is the remainder when \( (x+1)(x+3) \) is divided by 8? 0 1 3 6 7 Check Solution (D): We are given \(x \equiv 3 \pmod{8}\). Substitute this into the expression: \((x+1) \equiv (3+1) \equiv 4…

  • FM: Practise SET-2

    Factors & Multiples: Level 2 1. When the positive integer \(x\) is divided by 7, the remainder is 3. What is the remainder when \(2x^2\) is divided by 7? 1 2 3 4 6 Check Solution (E): We use remainder arithmetic. \(x \equiv 3 \pmod{7}\). We need \(2x^2 \pmod{7}\). \(x^2 \equiv 3^2 \equiv 9 \equiv…

  • OE: Practice SET-3

    GRE Math: Logic & Integers (Level 3) 1. If \(n = p \times q \times r\), where \(p, q,\) and \(r\) are distinct prime numbers, how many distinct positive factors does \(n^2\) have? 6 8 9 12 27 Check Solution (E): The number \(n\) is \(p^1 q^1 r^1\). Therefore, \(n^2 = (p^1 q^1 r^1)^2 =…

  • OE: Practice SET-2

    GRE Math: Logic & Integers (Level 2) 1. If \(a+b\) is even and \(b+c\) is odd, which of the following must be true? a is even b is odd c is even a+c is odd abc is even Check Solution (D): \(a+b\) is even \(\implies\) \(a, b\) have the same parity (both even or both…

  • UD: Practice SET-3

    GRE Math: Units & Remainders (Level 3) 1. What is the units digit of \( (17)^{17} \times (23)^{23} \)? 1 3 7 9 5 Check Solution (D): 1. For \(17^{17}\): Cycle for 7 is {7, 9, 3, 1}. \(17 \div 4 = 4\) remainder 1. This is the 1st step: 7. 2. For \(23^{23}\): Cycle…

  • UD: Practice SET-2

    GRE Math: Units & Remainders (Level 2) 1. What is the units digit of \(8^{102} + 3^{63}\)? 1 3 5 7 9 Check Solution (A): 1. For \(8^{102}\): Cycle is {8, 4, 2, 6}. \(102 \div 4 = 25\) remainder 2. This is the 2nd step: 4. 2. For \(3^{63}\): Cycle is {3, 9, 7,…