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

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.

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
_________________

(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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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.

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

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

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

∆ 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)

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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