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In the decimal representation of z above, x denotes the tenths digit o

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Bunuel
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In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 02:02
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z = 56.x43
In the decimal representation of z above, x denotes the tenths digit of z. Can x be equal to 2?

(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644
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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 04:12
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z = 56.x43
In the decimal representation of z above, x denotes the tenths digit of z. Can x be equal to 2?

x= 2 ?

(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
10z = 56x.43 = 564.0

x = 4 since tenth position is 4 < 5. NO
x can't take any value.

SUFFICIENT.

(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644
100z = 56x4.3 = 5644.0
x = 4 since all positions on left side remain same. NO
5644 can only be possible if x = 4 as any other value invalidates the condition.

SUFFICIENT.

Answer D.
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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 06:25
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Quote:
z = 56.x43
In the decimal representation of z above, x denotes the tenths digit of z. Can x be equal to 2?

(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644


(1) sufic

56.x43*10=56x.43
rounded integer: 564
since .4 rounds down, then x=4

(2) sufic

56.x43*100=56x4.3
rounded integer: 5644
since .3 rounds down, then x=4

Ans (D)
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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 06:39
IMO , D

z = 56.x43
In the decimal representation of z above, x denotes the tenths digit of z. Can x be equal to 2?

(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
10 Z = 564 .. => x must be 4 since 564.4 can be rounded to 564 -- sufficient

(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644

100 Z = 5644 => x must be 4 since 5644.3 can be rounded to 5644 -- sufficient
Hence D
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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 09:08
Ans D
With statement 1- we clearly know x is 4.
With statement 2- we know it is 4.

So with each statement individually we know it is not 2

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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  Updated on: 03 Jun 2020, 20:34
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z = 56.x43
For x to be equal to 2, if rounding up is done, x needs to be equal to 2 and no other digit.

(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
56.x43 * 10 = 56x.43 and given 56x.43 = 564
Thus, x = 4. Statement (1) is SUFFICIENT

(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644
56.x43 * 100 = 56x4.3 and given 56x4.3 = 5644
Thus, x = 4. Statement (2) is SUFFICIENT

Answer - D

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Originally posted by RajatJ79 on 03 Jun 2020, 20:32.
Last edited by RajatJ79 on 03 Jun 2020, 20:34, edited 1 time in total.
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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 20:32
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z = 56.x43
In the decimal representation of z above, x denotes the tenths digit of z. Can x be equal to 2?

(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644

1) 10*z= 56x.43 = 564
so x=4
sufficient

2) 100*z=56x4.3 = 5644
so x=4
sufficient

Ans D
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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink] New post  03 Jun 2020, 20:48
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Answer is D

Statement 1: When the product of 10 and z is rounded to the nearest integer, the result is 564
That means 10*56.x43 = 56x.43
Nearest integer to 56x.43 is 56x
Also, 56X=564
Therefore X can't be 2 (sufficient)

Statement 2: When the product of 100 and z is rounded to the nearest integer, the result is 5644
That means 100*56.x43 = 56x4.3
Nearest integer of 56x4.3 is 56x4 which is 5644.
Therefore x = 4
So, X can't be 2 (sufficient)

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Re: In the decimal representation of z above, x denotes the tenths digit o [#permalink]
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