The symbols, #, &, @, $, represent non zero digits. If #2

Question

I came across this Data Sufficiency question white taking an old Cambridge Test.

The symbols, #, &, @, $, represent non zero digits.

If #2 + 3& = @$ 
 
What is represented by @$

(1) # = 2x&
(2) 10 x@ + $ = 95

This problem can be solved using pen and putting some effort, but I am trying to avoid it. Here's my approach.

Considering (1)  - & can only be 1/ 2/ 3. It can not be 4, since # + 3 gives a single digit number @. But, that's all what we can conclude. So 1 alone is not sufficient.  1

Considering (2)  - $ has to be 5 and @ 9. Since we are multiplying by 10, @ will be the tens digit and $ the units digit.

That's what we want. So the answer will be 2.

We don't need to know the exact value. Since the multiplying value was 10, we easily came to know the value of the constants.

If you have some better method, please share.

Zarrolou · Answer

I agree with you, the answer shuold be B.

10@ + $ = 95

divide by 10

@+ 0,1$=9,5

@ is the unit digit => 9
$ is the first decimal => 5

Thoughtosphere · Answer

I didn't get you, how can you divide it by 10 and get @ + 0 ? :!:

Zarrolou · Answer

I didn't get you too: where did I write "@ + 0"? What do you mean?

We can see it this way

@ + $/10= 9 + 5/10

and because @ and $ are single digit numbers -> @=9 and $ = 5 is the only answer
In the and we have the same conclusion

Thoughtosphere · Answer

No we can not see it that way. @ + $/10 and (@ + $) / 10 are two completely different things. Consider numbers Let @ = 9, $ = 5. @ + $/10 would mean, 9.5 whereas (@ + $) / 10 would mean, 1.4 Hope it helps you... :-)

shanmugamgsn · Answer

I will give a try

#2 + 3& ---- @$ ---- i) # = 2x& this will not be much useful if &=2 #=4 (Note : here we are not mentioned all digits are distinct, if it so we can omit this) if &=3 #=6 (Note : here we are not mentioned all digits are distinct, if it so we can omit this) if &=4 #=8 ii)10 x@ + $ = 95 Since each symbol is single digit, at most @ can be 9, which leads to 10x9=90 + 5 =95 We got two numbers, now simple pluggin and get it solved 62 + 33 ---- 95 ---- pls let me know if im wrong

Thoughtosphere · Answer

You have hit the bulls eye.. :-D

shanmugamgsn · Answer

Thanks Buddy... Kudos will help

eddyki · Answer

1) no suff: # is max = 8 and min 4
& is max 4 and min 1
2) is suff: @ only possbility to be 5 (single Digit number)
$ can only be 9. (single Digit number multiplied by 10)

we need no calculation

bumpbot · Answer

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The symbols, #, &, @, $, represent non zero digits. If #2

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GMAT Data Sufficiency (DS) Questions

The symbols, #, &, @, $, represent non zero digits. If #2

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