If the symbols Δ and ◊ each represent digits in the following subtract

Question

If the symbols Δ and ◊ each represent digits in the following subtraction operation, what is the value of ◊?

Δ ◊ ◊ 
   - Δ Δ  
 6 6 7

A. 3
B. 4
C. 5
D. 8
E. 9

Gnpth · Accepted Answer

We need to first think values for Δ. As the result is in 600's, It cannot be less than 6.

If Δ is 6 then the range will be between 600 to 699. But if we subtract 66, will it be giving 667? No.So we need think for another value of Δ.

If Δ is 7, then the range of Δ ◊ ◊ will be between 700 and 799. And if we subtract ΔΔ(77) Some number in 700's will give 667. From this value we can get the value of ◊.

But instead of plugging in the values to find the ◊. We can add the 667 and 77 to get Δ ◊ ◊.

This will give us,

667+77 = 744. So ◊= 4

So the answer is B.

PareshGmat · Answer

Replacing the symbols with alphabets

abb - aa = 667 Expanding LHS 100a + 10b + b - (10a + a) = 667 89a + 11b = 667 Looking at the options: A: For b=3 89a = 667-33 = 634 If a = 6; then 634 should be divisible by 6.. its NOT; so discard How I selected 6??? For 89 to be multiplied by "a" & give the result ending with "4"; a should be 6 B: For b = 4 89a = 667 - 44 = 623 If a=7; 623 should be divisible by 7... 623/7 = 89 ......... SUCCESS Answer = B = 4

Bunuel · Answer

Similar questions to practice: PS: ab-cd-aaa-where-ab-and-cd-are-two-digit-numbers-and-aa-136903.html in-the-below-addition-a-b-c-d-e-f-and-g-represent-the-165187.html in-the-correctly-worked-addition-problem-shown-where-the-54154.html in-the-addition-shown-above-a-b-c-and-d-represent-161656.html DS: in-the-correctly-worked-addition-problem-above-a-b-c-d-128953.html if-in-the-addition-problem-above-a-b-c-d-e-f-x-y-a-97479.html Hope this helps.

Bunuel · Answer

Check other  Operations/functions defining algebraic/arithmetic expressions probelms  in our  Special Questions Directory .

BrainLab · Answer

Let's say Δ = x and ◊ = y. As you see we substract both times y-x but get 7 and 6 below, that means we had to borrow 1 by the first substraction. That also means that we need to borrow 1 also from x --> means x=6+1=7 and y+10-x=3, so y=x-3 = 7-3=4 
Answer B

BillyZ · Answer

The most difficult part of the first problem is simply getting started. Even though it is a subtraction problem, think of it as addition (667 + ∆∆ = ∆◊◊) and consider the following logic: If you add a two–digit number to 667, you must end up in the high 600s or the 700s. However, if the ∆ symbol is a 6, then you are adding 66 to 667, which will not work out, as the result will be in the 700s but the ∆ symbol has been designated as 6. Therefore the ∆ symbol must be a 7. At this point you can add 7 to 7 and see that the other symbol ◊ must be a 4 (7 plus 7 is 14). Check your work: 744 – 77 does indeed equal 667. The correct answer choice is B.

gps5441 · Answer

It is easier and faster to use the answer choices given to arrive at the correct answer.

Δ ◊ ◊ 
- Δ Δ 
6 6 7

A. 3
B. 4
C. 5
D. 8
E. 9

Let us say ◊ =5 plugin

Δ 5 5 
- Δ Δ 
6 6 7

Now when we subtract the units digit the digit obtained is 7. therefore Δ=8

8 5 5 
- 8 8
7 6 7

Do we get 6 in Hundreds digit-NO. Hence 5 is the wrong answer

Try 4
Δ 4 4 
- Δ Δ 
6 6 7

If ◊=4 than Δ=7. Now plugin
7 4 4 
- 7 7 
6 6 7

We have our answer=B=4

SpartanX · Answer

Given:
^ * *
- ^ ^
------
6 6 7

Rearrange:
 6 6 7
+ ^ ^
-------
^ * *

We can notice that ^ must be 6 or 7 considering the thousandths digit in the result.
Solve for ^ = 6, we get 733.
The unit and tenth digits are same but ^ changes to 7. So reject 6.

Solve for ^ = 7, we get 744.
The unit and tenth digits are same and ^ remains 7. So the answer * is 4.

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If the symbols Δ and ◊ each represent digits in the following subtract

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