GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Every digit of a number written in binary is either 0 or 1. To transla
[#permalink]
04 Jun 2021, 23:23
04 Jun 2021, 23:23
Expert Reply
00:00
Question Stats:
0% (00:00) correct
100% (03:54) wrong based on 2 sessions
Hide Show timer Statistics
Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1). What is the largest prime number (written in binary) that is a factor of both 100010000 and 1000100000 ?
(A) 10
(B) 11
(C) 101
(D) 1011
(E) 10001
(A) 10
(B) 11
(C) 101
(D) 1011
(E) 10001
Every digit of a number written in binary is either 0 or 1. To transla
[#permalink]
06 Jun 2021, 02:39
06 Jun 2021, 02:39
2
A very much time wasting question :
We are given all the numbers in binary. To convert in decimal multiply the nth digit (reading from right to left) by \(2^{n-1}\).
The largest prime that is a factor of both 100010000 and 1000100000
Converting them into decimals, we will get
(100010000)₂ = (1×2⁸) + (0×2⁷) + (0×2⁶) + (0×2⁵) + (1×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (0×2⁰) = \(272\)
(1000100000)₂ = (1×2⁹) + (0×2⁸) + (0×2⁷) + (0×2⁶) + (1×2⁵) + (0×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (0×2⁰) = \(544\)
Now,
(A) 10 :: (10)₂ = (1×2¹) + (0×2⁰) = \((2)₁₀\) Can divide but is not the largest.
(B) 11 :: (11)₂ = (1×2¹) + (1×2⁰) = \((3)₁₀\) Can't divide
(C) 101 :: (101)₂ = (1×2²) + (0×2¹) + (1×2⁰) = \((5)₁₀\) Can't divide
(D) 1011 :: (1011)₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = \((11)₁₀\) Can't divide
(E) 10001 :: (10001)₂ = (1×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (1×2⁰) = \((17)₁₀\) Answer
We are given all the numbers in binary. To convert in decimal multiply the nth digit (reading from right to left) by \(2^{n-1}\).
The largest prime that is a factor of both 100010000 and 1000100000
Converting them into decimals, we will get
(100010000)₂ = (1×2⁸) + (0×2⁷) + (0×2⁶) + (0×2⁵) + (1×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (0×2⁰) = \(272\)
(1000100000)₂ = (1×2⁹) + (0×2⁸) + (0×2⁷) + (0×2⁶) + (1×2⁵) + (0×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (0×2⁰) = \(544\)
Now,
(A) 10 :: (10)₂ = (1×2¹) + (0×2⁰) = \((2)₁₀\) Can divide but is not the largest.
(B) 11 :: (11)₂ = (1×2¹) + (1×2⁰) = \((3)₁₀\) Can't divide
(C) 101 :: (101)₂ = (1×2²) + (0×2¹) + (1×2⁰) = \((5)₁₀\) Can't divide
(D) 1011 :: (1011)₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = \((11)₁₀\) Can't divide
(E) 10001 :: (10001)₂ = (1×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (1×2⁰) = \((17)₁₀\) Answer
gmatclubot
Every digit of a number written in binary is either 0 or 1. To transla [#permalink]
06 Jun 2021, 02:39
Moderators:
