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555-605 Level|   Arithmetic|               
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Bunuel
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Data to be derived from question. All the 3 figures are positive digit. Hence these numbers can be only between 1&9 (inclusive) and will be distinct as one as the square is smaller than triangle, which means both are different digits and adding two different +VE digits will give you a 3rd digit that is different from previous 2.

S(1): *=4. The possible combinations are 3,1 1,3 & 2,2. Since we know triangle is bigger than square it only leaves us with 1,3. Hence Suff.

S(2) Square=1. Which means triangle can be any number between 2-8 to satisfy above conditions. Hence N.S.

THus answer is A.
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Bunuel

Tough and Tricky questions: Arithmetic.




+△
___

In the addition problem above, each of the symbols □, △, and ★ represents a positive digit. If □ < △,what is the value of △ ?

(1) ★ = 4
(2) □ = 1

Kudos for a correct solution.


From Statement 1: ★=4; which Will give only one combination of □ and △ (1,3) since □ is less than △, △ should be 3 - Sufficient
Statement 2: □ = 1 from this △ can be any value greater than 1-not sufficient


Ans A
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Bunuel

Tough and Tricky questions: Arithmetic.




+△
___

In the addition problem above, each of the symbols □, △, and ★ represents a positive digit. If □ < △,what is the value of △ ?

(1) ★ = 4
(2) □ = 1

Kudos for a correct solution.

The correct answer is A.

Check other Addition/Subtraction/Multiplication Tables problems from our Special Questions Directory
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gjonrexha
Where in the problem does it state that the number has to be an integer? All it says is that the three symbols correspond to a positive digit so the Triangle and Square can be any infinite number of combinations -1 (since the triangle is bigger) therefore the answer must be C.

There are only 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are told that symbols represent positive digits, so they can be 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Check more on number theory here: https://gmatclub.com/forum/math-number-theory-88376.html

Hope it helps.
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Great work as usual Bünuel that helped a lot !


Sent from my iPhone using GMAT Club Forum
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In the addition problem given, each of the symbols □, △, and ★ represents a positive digit. If □ < △,we need to find the value of △.

(1) Sufficient:★ = 4, Addition of 1+3 and 3+1 results in 4 but since □ < △ hence only □ =1 and △=3 is valid.
(2) Insufficient: □ = 1,In this case △ and ★ can take multiple values such as 1+2=3,1+3=4..etc

IMO A is the correct answer.
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Bunuel, KarishmaB

My question is ,"Can the digit be negative or non negative? "

A number can be such but a digit is neutral. When we say that it represents digit, 0 should have been considered as a digit irrespective of positive or negative. I hope that tags of this question are correct as it seems to be an official question as per the tags added. I found it little difficult to digest that here 0 cannot be considered since the question stems says symbols represent positive digit. Because of that answer would have been completely different.
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Bunuel, KarishmaB

My question is ,"Can the digit be negative or non negative? "

A number can be such but a digit is neutral. When we say that it represents digit, 0 should have been considered as a digit irrespective of positive or negative. I hope that tags of this question are correct as it seems to be an official question as per the tags added. I found it little difficult to digest that here 0 cannot be considered since the question stems says symbols represent positive digit. Because of that answer would have been completely different.

The word "digit" is applicable to the ten digits 0 to 9.
Out of these, one digit (0), is neither negative nor positive.
The other nine digits (1 to 9) are positive.
All digits are non negative.

Hence, the point of saying "positive digit" is to tell you that no symbol can be 0.
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Hi Bunuel, thanks for the question! I am confused about how we can assume that the square and triangle are necessarily different digits. Any clarification would be much appreciated!
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Hi Bunuel, thanks for the question! I am confused about how we can assume that the square and triangle are necessarily different digits. Any clarification would be much appreciated!

It's given in the stem:


+△
___


In the addition problem above, each of the symbols □, △, and ★ represents a positive digit. If □ < △,what is the value of △ ?

(1) ★ = 4
(2) □ = 1
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+△
___


And it is given that □ < △

STAT 1: ★ = 4

=> Sum of two positive digits = 4
=> Possible cases are (1 , 3) , (2,2) , (3,1)

But □ < △
=> □ = 1 and △ = 3
=> SUFFICIENT

STAT 2: □ = 1

We know that □ < △
But △ can be any number > 1 and < 9 to make the sum ★ a positive digit
=> NOT SUFFICIENT

So, Answer will be A
Hope it helps!
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