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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

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Bunuel
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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   20 Oct 2019, 21:48
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C
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E

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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
(2) When rounded to the nearest tenth, the decimal becomes ∆.O
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C
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   20 Oct 2019, 22:02
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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
So \(O\geq{5}\), as ∆.O∆ becomes O when rounded to nearest integer. Also ∆+1=O, as ∆ converts to O.
But the decimal could be 4.54 or 5.65 or 6.76 or 7.87 or 8.98.. so the value of ∆ could be in the range \(4\leq{∆}\leq{8}\)

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
This tells us that ∆<5 as the tenth digit does not change, so range becomes \(0\leq{∆}\leq{4}\)

Combined..
∆ will be 4, and the number is 4.54

C
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   Updated on: 20 Oct 2019, 22:26
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Given ∆.O∆, where ∆ and O are distinct digits. We are to determine ∆.

From statement 1, rounding ∆.O∆ to the nearest integer yields O
For this to occur, we know O must have the following possible values: 5,6,7,8,9
while ∆ can be any of the following: 4,5,6,7,8,9
There are many possibilities for ∆ hence statement 1 is not sufficient on its own.

From Statement 2, rounding ∆.O∆ to the nearest tenth decimal yields ∆.O
this implies ∆ is less than 5. hence ∆ can be 1,2,3,4
Statement 2 is not sufficient.

1+2
means ∆ = 4. This is because 4 is the only common possible value in both statements.
Both statements taken together are sufficient to answer the question.

The answer is therefore C.

Originally posted by eakabuah on 20 Oct 2019, 22:25.
Last edited by eakabuah on 20 Oct 2019, 22:26, edited 1 time in total.
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   20 Oct 2019, 22:26
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Given: Let ∆ and O be two distinct digits in the decimal ∆.O∆

Asked: what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
O = ∆ + 1
∆ >= 4
∆ = {4,5,6,7,8}
There may be many such pairs
NOT SUFFICIENT

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
∆ < 5
∆ = {0,1,2,3,4}
NOT SUFFICIENT

(1) + (2)
(1) When rounded to the nearest integer, the decimal becomes O
O = ∆ + 1
∆ = {4,5,6,7,8}
(2) When rounded to the nearest tenth, the decimal becomes ∆.O
∆ < 5
∆ = {0,1,2,3,4}
∆ = 4
Only 4.54 satisfy both conditions
SUFFICIENT

IMO C
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   20 Oct 2019, 22:45
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(1) When rounded to the nearest integer, the decimal becomes O
Then values of ∆ and O will be.... ∆= O-1where O=5,6,7,8,9 and ∆= 4,5,6,7,8.....So insufficient


(2) When rounded to the nearest tenth, the decimal becomes ∆.O

Then ∆ =0,1,2,3,4.....So insufficient



From both we can get ∆=4 , O=5

4.54


OA:C

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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   20 Oct 2019, 22:52
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
Rounded to nearest integer, the decimal should be .0
Therefore, O = 0
However, we do not know anything about ∆ - INSUFFICIENT

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
Rounded to nearest integer, the decimal becomes as above, we can infer that ∆ is between 0 - 4, but we dont know which number. - INSUFFICIENT

Taken (1) + (2) together, insufficient because we do not know ∆

Thus, E is the correct answer choice.
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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   Updated on: 22 Oct 2019, 02:52
given ∆.O∆
find value of ∆
#1
When rounded to the nearest integer, the decimal becomes O
it means that ∆ is 1,2,3,4
insufficient
#2

When rounded to the nearest tenth, the decimal becomes ∆.O
∆ can be 1,2,3,4 and O can be any integer value 0-9 insufficeint
from 1&2
∆=4 and O = 5
4.54
sufficient IMO C

Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
(2) When rounded to the nearest tenth, the decimal becomes ∆.O

Originally posted by Archit3110 on 21 Oct 2019, 01:59.
Last edited by Archit3110 on 22 Oct 2019, 02:52, edited 1 time in total.
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   21 Oct 2019, 04:48
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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(Statement1): When rounded to the nearest integer, the decimal becomes O
∆.O∆- could be:
--> 4.54≈5
--> 5.65≈6
--> 6.76≈7
...
----------
4≤ ∆≤8

Insufficient

(Statement2): When rounded to the nearest tenth, the decimal becomes ∆.O
--> 2.52 ≈2.5
--> 3.43 ≈3.4
--> 4.54 ≈4.5
...
--------------
1≤ ∆≤ 4
Insufficient

Taken together 1&2,
Only ∆=4 satisfies the both statements

--> 4.54 ≈5 (statement1)
--> 4.54 ≈4.5 (statement2)

Sufficient

The answer is C
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   21 Oct 2019, 05:46
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Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
meaning, ∆=O-1 and O> or =5
∆ can be 4,5,6,7,8
insufficient

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
∆ can be 0,1,2,3,4
insufficient

Together, ∆ must be 4
Therefore, C
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   21 Oct 2019, 07:13
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Quote:
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
(2) When rounded to the nearest tenth, the decimal becomes ∆.O


∆ and O are two DISTINCT digits

(1) When rounded to the nearest integer, the decimal becomes O insufic.

round.integer(∆.O∆)=O; so O=∆+1≥5
if ∆.O∆=4.54 rounded=5; (O,∆)=(5,4)
if ∆.O∆=5.65 rounded=5; (O,∆)=(6,5)

(2) When rounded to the nearest tenth, the decimal becomes ∆.O insufic.

round.tenth(∆.O∆)=∆.O; so ∆≤4={0,1,2,3,4}

(1 & 2) sufic.

O=∆+1≥5…∆+1≥5…∆≥4 and ∆≤4…∆=4…O=5

Answer (C)
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Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆? [#permalink] New post   21 Oct 2019, 12:54
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While rounding number increases if digit after decimal is greater than equal to 5 i.e., 5,6,7,8,9 else it will be same i.e., for 0 1,2,3,4

Now to question
1) When rounded to the nearest integer, the decimal becomes O
0 can have value 5,6,7,8,9 but at the same time ∆ has to be 4,5,6,7,8.
Therefore not sufficient

2) When rounded to the nearest tenth, the decimal becomes ∆.O
Implies that ∆ has to be less than 5 {0,1,2,3,4} Therefore not sufficient

Combining 1 and 2
∆ = 4

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Re: Let and O be two distinct digits in the decimal .O, what is ? [#permalink] New post   09 Oct 2023, 23:37
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Re: Let and O be two distinct digits in the decimal .O, what is ? [#permalink]
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