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

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Thoughtosphere
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The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   Updated on: 06 Mar 2013, 03:12
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

62% (02:21) correct 38% (02:06) wrong based on 100 sessions
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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

Show Spoiler
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.
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Official Answer
B

Originally posted by Thoughtosphere on 06 Mar 2013, 03:05.
Last edited by Bunuel on 06 Mar 2013, 03:12, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   06 Mar 2013, 03:43
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
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   06 Mar 2013, 04:37
Zarrolou wrote:
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


I didn't get you, how can you divide it by 10 and get @ + 0 ? :!: :!: :!:
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   06 Mar 2013, 05:03
Thoughtosphere wrote:
Zarrolou wrote:
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


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


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
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   06 Mar 2013, 23:15
Zarrolou wrote:
Thoughtosphere wrote:
Zarrolou wrote:
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


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


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


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... :-)
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   07 Mar 2013, 00:22
Thoughtosphere wrote:
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

Show Spoiler
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.


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
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Thoughtosphere
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   07 Mar 2013, 01:42
shanmugamgsn wrote:
Thoughtosphere wrote:
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

Show Spoiler
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.


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


You have hit the bulls eye.. :-D
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shanmugamgsn
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   10 Mar 2013, 07:07
Thanks Buddy...

Kudos will help :P
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eddyki
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Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink] New post   13 Jan 2015, 08:01
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
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gmatclubot
Re: The symbols, #, &, @, $, represent non zero digits. If #2 [#permalink]
13 Jan 2015, 08:01
Moderator:
Bunuel
Math Expert
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