If d is the thousandth’s digit in the decimal above, what is the value

Question

x = 1.24d5
If d is the thousandth’s digit in the decimal above, what is the value of x when rounded to the nearest hundredth?

(1) x < 5/4
(2) d < 5

chetan2u · Answer

Hi,

when x is rounded to the nearest hundreth, x will be 1.25 if x>=5 and x will be 1.24 if x<5..

(1) x < 5/4
x < 1.25, so x can be 1.2495.. ans will be 1.25
or x can be 1.2415... ans will be 1.24
Insuff

(2) d < 5
since d<5.. x will be 1.2405 or 1.2415 or 1.2425 or 1.2435 or 1.2445..
In all cases x will give ans as 1.24
Suff

B

PKay · Answer

Statement 1: x<5/4 (1.25)
the value of X can be 1.24 only cause he said that X is rounded nearest hundredth digit. It cannot be any other value a.k.a 1.23 or 1.26 as per the question
X!= 1.25 or 1.26. It can only be 1.24 when rounded to hundredth place
Hence Statement 1 alone also sufficient

chetan2u · Answer

Hi,

I am sorry I do not understand what you meant by that since it is being rounded to hundredths, it can only be 1.24...
 rounding off to hundredths DEPENDS on thousandths place.. 
and from  x<\frac{5}{4}......x<1.25 , we cannot guess thousandths place..
let me tell you with an example..
x = 1.2495..... 1.2495<1.25, But when you round off 1.2495 to nearest hundredth, it will be 1.25..
if x = 1.2415......1.2415<1.25, But when you round off 1.2415 to nearest hundredth, it will be 1.24..

I do understand that OA is D, but I have not understood WHY it should be D and I am sorry, You may be correct but I have not understood the logic which you have given..

Divyadisha · Answer

(1) x < 5/4 
x<1.25
Looking at the expression x can be > or = 1.24. Hence x= 1.24 when rounded to nearest hundredth

Sufficient

(2) d < 5

If d<5, then hundredth digit will not increase by 1. Sufficient.

D is the answer

Kurtosis · Answer

Even I agree with  chetan2u . I think the OA must be B.

St1: Value of x < 1.25 --> d can take any value between 0 to 9
1.2405 < x < 1.2495
Rounded value of x can be either 1.24 or 1.25

If St1 was modified as Rounded value of x < 1.25 then answer D would be acceptable.

PKay · Answer

Statement 1: x<5/4 (1.25) the value of X can be 1.24 only cause he said that X is rounded nearest hundredth digit. It cannot be any other value a.k.a 1.23 or 1.26 as per the question X!= 1.25 or 1.26. It can only be 1.24 when rounded to hundredth place Hence Statement 1 alone also sufficient Hi, I am sorry I do not understand what you meant by that since it is being rounded to hundredths, it can only be 1.24... rounding off to hundredths DEPENDS on thousandths place.. and from x<\frac{5}{4}......x<1.25 , we cannot guess thousandths place.. let me tell you with an example.. x = 1.2495..... 1.2495<1.25, But when you round off 1.2495 to nearest hundredth, it will be 1.25.. if x = 1.2415......1.2415<1.25, But when you round off 1.2415 to nearest hundredth, it will be 1.24.. I do understand that OA is D, but I have not understood WHY it should be D and I am sorry, You may be correct but I have not understood the logic which you have given.. x= 1.24d5 Case 1: d>= 5, then x=1.25 (rounded off to hundredth place) Case 2: d<5, then x=1.24 (rounded off to hundredth place) Statement 1: x<5/4 => x<1.25 The question says "If d is the thousandth’s digit in the decimal above, what is the value of x when rounded to the nearest hundredth?" only 2 values of x are possible after rounding off (as I said earlier) -1.25 or 1.24 But as per the statement x<1.25. so x has to be equal to 1.24 Statement 2: when d<5, x=1.24 after rounding off to hundredth place. Both individually sufficient. Hence D I hope its clear now. Cheers PK

Kurtosis · Answer

Hi  peekaysan ,

Why are you assuming 'x' given in St1 to be the rounded value of x?

Values of x can range between 1.2405 and 1.2495 as per Statement 1.

fantaisie · Answer

I would also agree with Vyshak & chetan2u.

We know that x (the entire number, no one has indicated that it refers to the rounded number), x<1.25
x can still be x=1.2595 which is less than 1.2500 but also could be 1.2535, which is also less than 1.2500.

In both cases, x to the hundreth will be different. The answer should be B.

chetan2u · Answer

Thanks PK for taking so much efforts...
But you are forgetting x < 1.25 and not "rounded off value of x"< 1.25.....
so what does it mean..
x is not only 1.24 and 1.25, it can be anything 1.2405, 1.2415,... till 1.2495..

I hope it helps you now in understanding the POINT here.

As I told you don't go by OA, it may just be typing error, go by logic and there could be some other reason, but it is certainly not what you have mentioned

sudhirmadaan · Answer

I do agree with answer as B.
x is less than 5/4 not the rounded value of x

Bunuel  please explain.

PKay · Answer

I get it. I misunderstood the question. :oops:

stonecold · Answer

Great Question..!
here when we round x to nearest hundredths we will either get=>
1.24 for d≤4
OR
1.24 for d≥5
hence we need the value of d

Statement 1
This statement will always hold true for any value of d
hence not sufficient 
statement 2
From this statement we can state with authority that x rounded to nearest hundredths will always be 1.24
hence sufficient 
hence B

Dekstar · Answer

Bunuel, I think the answer here is "D"

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If d is the thousandth’s digit in the decimal above, what is the value

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If d is the thousandth’s digit in the decimal above, what is the value

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