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In the addition problem above, each of the symbols , , and represe

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Bunuel
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In the addition problem above, each of the symbols , , and represe [#permalink] New post   22 Dec 2014, 09:04
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A
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C
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E

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25% (medium)

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70% (01:15) correct 30% (01:19) wrong based on 2341 sessions
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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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   30 Jan 2017, 17:44
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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.
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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   22 Dec 2014, 10:17
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In the addition problem above, each of the symbols □, △, and ★ represents a positive digit. If □ < △,what is the value of △ ?

Statement 1: ★ = 4
Given □ < △, only one possibility □ = 1 and △ = 3 -- Sufficient

Statement 2: □ = 1
△ can be {2,3,4,5,6,7,8} -- Insufficient

Answer A
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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   22 Dec 2014, 20:37
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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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   23 Dec 2014, 11:29
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Bunuel wrote:

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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   24 Dec 2014, 08:11
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Bunuel wrote:

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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   31 Jan 2017, 07:40
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gjonrexha wrote:
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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   02 Feb 2017, 20:15
Great work as usual Bünuel that helped a lot !


Sent from my iPhone using GMAT Club Forum
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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   02 Sep 2021, 07:43
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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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   24 Dec 2021, 21:33
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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   26 Dec 2021, 21:51
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brains wrote:
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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   26 Jun 2022, 22:25
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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   27 Jun 2022, 01:48
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saranshgokhale wrote:
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:

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+△
___
★

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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Re: In the addition problem above, each of the symbols , , and represe [#permalink] New post   10 Dec 2023, 20:54
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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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Re: In the addition problem above, each of the symbols , , and represe [#permalink]
10 Dec 2023, 20:54
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