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# If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x

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Joined: 12 May 2017
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If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 07:42
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61% (01:44) correct 39% (01:19) wrong based on 38 sessions

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If $$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$. What is the value of x+y+z+t?

A. 7
B. 15
C. 20
D. 30
E. 35
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Posts: 2948
Location: India
GPA: 3.12
If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 08:25
div10 wrote:
If $$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$. What is the value of x+y+z+t?

A. 7
B. 15
C. 20
D. 30
E. 35

We can solve the problem by using the pascals triangle - The coefficients(the numbers in front of each term) follow a pattern

1
$$(a+b)^0 = 1$$

1 1
$$(a+b)^1 = a + b$$

1 2 1
$$(a+b)^2 =a^2 + 2ab +b^2$$

1 3 3 1
$$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$

1 4 6 4 1
$$(a + b)4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b4$$

1 5 10 10 5 1
$$(a+b)^5 = a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$$

Therefore, Value of x+y+z+t = $$5+10+10+5 = 30$$(Option D)
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Posts: 6261
Re: If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 09:23
div10 wrote:
If $$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$. What is the value of x+y+z+t?

A. 7
B. 15
C. 20
D. 30
E. 35

Hi...

any expansion is ..
$$(a+b)^n = nC0a^nb+nC1a^{n-1}b^1........+nCnb^n$$
and when you add the coefficient $$nC0+nC1+...nCn=2^n$$

here n is 5..
$$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$
so addition of coefficients = $$2^5=1+x+y+z+t+1......32=2+x+y+z+t$$
so $$x+y+z+t =32-2=30$$

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 09:43
chetan2u wrote:
div10 wrote:
If $$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$. What is the value of x+y+z+t?

A. 7
B. 15
C. 20
D. 30
E. 35

Hi...

any expansion is ..
$$(a+b)^n = nC0a^nb+nC1a^{n-1}b^1........+nCnb^n$$
and when you add the coefficient $$nC0+nC1+...nCn=2^n$$

Just wondering if this is in scope in GMAT?
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Posts: 6261
Re: If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 09:45
saswata4s wrote:
chetan2u wrote:
div10 wrote:
If $$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$. What is the value of x+y+z+t?

A. 7
B. 15
C. 20
D. 30
E. 35

Hi...

any expansion is ..
$$(a+b)^n = nC0a^nb+nC1a^{n-1}b^1........+nCnb^n$$
and when you add the coefficient $$nC0+nC1+...nCn=2^n$$

Just wondering if this is in scope in GMAT?

No, not really..
But $$nC0+nC1+nC2+...nC(n-1)+nCn= 2^n$$ can make some Q easier although there would be some other way too to solve it.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 25 Feb 2013
Posts: 1183
Location: India
GPA: 3.82
Re: If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 09:46
div10 wrote:
If $$(a+b)^5=a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5$$. What is the value of x+y+z+t?

A. 7
B. 15
C. 20
D. 30
E. 35

Binomial theorem has never been asked in the GMAT. The question per-say is not difficult if one knows the binomial theorem or expansion till power 5

Hi Bunuel, is there any other way to solve the problem?
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Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
Re: If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x  [#permalink]

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25 Oct 2017, 09:54
chetan2u wrote:
No, not really..
But $$nC0+nC1+nC2+...nC(n-1)+nCn= 2^n$$ can make some Q easier although there would be some other way too to solve it.

Hmm, I agree. But I almost forgot all the concepts of binomial series and theorem, so this question really scared me
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Re: If (a+b)^5= a^5+xa^4b+ya^3b^2+za^2b^3+tab^4+b^5 What is the value of x &nbs [#permalink] 25 Oct 2017, 09:54
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