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12 Oct 2020, 04:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:49) correct
33%
(02:51)
wrong
based on 297
sessions
History
Date
Time
Result
Not Attempted Yet
\(\clubsuit x \clubsuit y \clubsuit = (2x-y)^2\)
\(\spadesuit a \spadesuit b \spadesuit = (a+2b)^2\)
If \(\spadesuit 5 \spadesuit (n-1) \spadesuit = 5n^2+4n\) and \(n< 6\), then \(\clubsuit 2n \clubsuit 2 \clubsuit =\)
A. 4
B. 9
C. 16
D. 36
E. 49
\(\spadesuit a \spadesuit b \spadesuit = (a+2b)^2\)
If \(\spadesuit 5 \spadesuit (n-1) \spadesuit = 5n^2+4n\) and \(n< 6\), then \(\clubsuit 2n \clubsuit 2 \clubsuit =\)
A. 4
B. 9
C. 16
D. 36
E. 49
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 10 Aug 2026
Posts: 3,095
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
12 Oct 2020, 08:28
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Given: ♣x♣y♣=(2x−y)^2
♠a♠b♠=(a+2b)^2
If ♠5♠(n−1)♠=5n^2+4n and n<6,
To find: ♣2n♣2♣=
Solution: ♠5♠(n−1)♠=5n^2+4n
{5+2(n-1)}^2 = 5n^2+4n
{5+2n-2}^2 = 5n^2+4n
{3+2n}^2 = 5n^2+4n
9+4n^2+12n = 5n^2+4n
9+8n = n^2
n^2-8n-9 = 0
n^2-9n+n-9 = 0
n(n-9)+1(n-9) =0
(n-9)(n+1) =0
n = 9 & -1
since n < 6
n = -1
♣2n♣2♣ => ♣2(-1)♣2♣
=> ♣-2♣2♣ = {2(-2)−2}^2
=> {-4-2}^2
=>{-6}^2
=> 36
Answer is D
♠a♠b♠=(a+2b)^2
If ♠5♠(n−1)♠=5n^2+4n and n<6,
To find: ♣2n♣2♣=
Solution: ♠5♠(n−1)♠=5n^2+4n
{5+2(n-1)}^2 = 5n^2+4n
{5+2n-2}^2 = 5n^2+4n
{3+2n}^2 = 5n^2+4n
9+4n^2+12n = 5n^2+4n
9+8n = n^2
n^2-8n-9 = 0
n^2-9n+n-9 = 0
n(n-9)+1(n-9) =0
(n-9)(n+1) =0
n = 9 & -1
since n < 6
n = -1
♣2n♣2♣ => ♣2(-1)♣2♣
=> ♣-2♣2♣ = {2(-2)−2}^2
=> {-4-2}^2
=>{-6}^2
=> 36
Answer is D
12 Oct 2020, 20:51
Kudos
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♣x♣y♣=(2x−y)^2
♠a♠b♠=(a+2b)^2
If ♠5♠(n−1)♠=5n^2+4n and n<6, then ♣2n♣2♣=
A. 4
B. 9
C. 16
D. 36
E. 49
Explanation: As ♠a♠b♠=(a+2b)^2
then ♠5♠(n−1)♠= {5+2(n-1)}^2
but given ♠5♠(n−1)♠=5n^2+4n
means 5n^2+4n={5+2(n-1)}^2
on simplifying both the sides,we get
n^2-8n-9=0
(n-9)(n+1)=0
thus n=-1 (rejecting n=9 as given n<6)
now
♣2n♣2♣=(4n-2)^2 (given ♣x♣y♣=(2x−y)^2 )
=(4*(-1)-2)^2
=36
Hence D is the correct answer
♠a♠b♠=(a+2b)^2
If ♠5♠(n−1)♠=5n^2+4n and n<6, then ♣2n♣2♣=
A. 4
B. 9
C. 16
D. 36
E. 49
Explanation: As ♠a♠b♠=(a+2b)^2
then ♠5♠(n−1)♠= {5+2(n-1)}^2
but given ♠5♠(n−1)♠=5n^2+4n
means 5n^2+4n={5+2(n-1)}^2
on simplifying both the sides,we get
n^2-8n-9=0
(n-9)(n+1)=0
thus n=-1 (rejecting n=9 as given n<6)
now
♣2n♣2♣=(4n-2)^2 (given ♣x♣y♣=(2x−y)^2 )
=(4*(-1)-2)^2
=36
Hence D is the correct answer
