If the symbols Δ and ◊ each represent digits in the following subtract : Problem Solving (PS)

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

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If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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01 Aug 2014, 02:21

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75% (02:09) correct

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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

Spoiler: OA

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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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01 Aug 2014, 07:05

pratikshr wrote:

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

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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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01 Aug 2014, 03:10

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
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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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01 Aug 2014, 02:40

pratikshr wrote:

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

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.
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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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23 Aug 2015, 04:58

pratikshr wrote:

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

Check other Operations/functions defining algebraic/arithmetic expressions probelms in our Special Questions Directory.
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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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20 Feb 2016, 04:04

pratikshr wrote:

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

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
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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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30 Apr 2017, 21:15

pratikshr wrote:

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

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.
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If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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20 Jul 2017, 19:52

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

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Re: If the symbols Δ and ◊ each represent digits in the following subtract [#permalink]

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05 Sep 2019, 12:29

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