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5 5 5
Last digit is "5"
7+5=_2
7+8=_5
7+9=_6
7+4=_1
5+8=_3
5+9=_4
5+4=_9
8+9=_7
8+4=_2
9+4=_3
We can only form Unit Digit as "5" by having unit digits as "7" & "8"
So, numbers _ _ 7 and _ 8 or vice versa
Now, we need to form Tens digit as "4" --> possible combinations: 5 & 9
So, numbers _ 5 _ and 9 _ or vice versa
Hundred's digit = 4
So, number 4 _ _
So, total pairs:
--> 457 & 98
--> 458 & 97
--> 497 & 58
--> 498 & 57
Answer [spoiler]{D}[/spoiler]
Last digit is "5"
7+5=_2
7+8=_5
7+9=_6
7+4=_1
5+8=_3
5+9=_4
5+4=_9
8+9=_7
8+4=_2
9+4=_3
We can only form Unit Digit as "5" by having unit digits as "7" & "8"
So, numbers _ _ 7 and _ 8 or vice versa
Now, we need to form Tens digit as "4" --> possible combinations: 5 & 9
So, numbers _ 5 _ and 9 _ or vice versa
Hundred's digit = 4
So, number 4 _ _
So, total pairs:
--> 457 & 98
--> 458 & 97
--> 497 & 58
--> 498 & 57
Answer [spoiler]{D}[/spoiler]
R A H U L
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Rakesh,rakeshd347 wrote:Please explain the best way to solve this.
Start it from Unit digit.
Which numbers added to give 5 at end {8,7} (one carry over to the ten's digit)
Coming to tens digit, which number adds up to give 4{9,5}
Coming to Hundredth Digit, There is only one possibility i.e. 4
so now,
497
58
498
57
457
98
458
97
Hence OA is 4
May I know what is OA ?
Regards,
Uva.
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There's an insight here that solves the problem immediately, given these answer choices. Here it is: You're given a SUM. If you switch digits in the same decimal place, the sum is unchanged.
For instance, if you have xxxxx7 + yyyyy5, then that's the same as xxxxx5 + yyyyy7. And so on with the tens digits.
Why would we care?
Well...
You know there's at least one solution.
But, as soon as there's one solution:
* You can switch the units digits (--> another solution).
* You can switch the tens digits (--> another solution).
* You can switch the tens digts AND switch the units digits (--> another solution).
You know these are all different solutions, because no digit appears more than once. Furthermore, given any solution, you could always do the same thing.
So, solutions are going to appear in groups of four.
The only multiple of four here is 4. Done.
--
If you don't have the above insight, then just start listing out possibilities, as the posters have done nicely above.
For instance, if you have xxxxx7 + yyyyy5, then that's the same as xxxxx5 + yyyyy7. And so on with the tens digits.
Why would we care?
Well...
You know there's at least one solution.
But, as soon as there's one solution:
* You can switch the units digits (--> another solution).
* You can switch the tens digits (--> another solution).
* You can switch the tens digts AND switch the units digits (--> another solution).
You know these are all different solutions, because no digit appears more than once. Furthermore, given any solution, you could always do the same thing.
So, solutions are going to appear in groups of four.
The only multiple of four here is 4. Done.
--
If you don't have the above insight, then just start listing out possibilities, as the posters have done nicely above.
Ron has been teaching various standardized tests for 20 years.
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lunarpower wrote:There's an insight here that solves the problem immediately, given these answer choices. Here it is: You're given a SUM. If you switch digits in the same decimal place, the sum is unchanged.
For instance, if you have xxxxx7 + yyyyy5, then that's the same as xxxxx5 + yyyyy7. And so on with the tens digits.
Why would we care?
Well...
You know there's at least one solution.
But, as soon as there's one solution:
* You can switch the units digits (--> another solution).
* You can switch the tens digits (--> another solution).
* You can switch the tens digts AND switch the units digits (--> another solution).
You know these are all different solutions, because no digit appears more than once. Furthermore, given any solution, you could always do the same thing.
So, solutions are going to appear in groups of four.
The only multiple of four here is 4. Done.
--
If you don't have the above insight, then just start listing out possibilities, as the posters have done nicely above.
Ron,
Awesome Explanation!(Simple and clear)
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Thanks.Awesome Explanation!(Simple and clear)
(My brain doesn't really understand things unless they are simple. On this test, that's a huge advantage.)
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
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maybe this is a reason why you like teaching us the analogy technique (making superior guys digestible)lunarpower wrote:
My brain doesn't really understand things unless they are simple. On this test, that's a huge advantage.
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I use analogies because the human brain is fundamentally wired for analogies/examples/experience, and not for rules.ngalinh wrote:maybe this is a reason why you like teaching us the analogy technique (making superior guys digestible)
Think about how you learn your first language, of which your knowledge is incredibly thorough. (Even if a professional linguist studies your language for years and years, (s)he will not approach anywhere near the level of competency you had in it when you were 11-12 yearsold.)
How many "rules" for your first language do you learn growing up? Zero. None. Just endless exposure to tons and tons of examples (from your parents, your friends, and whomever else).
Growing up, even if you see something stated in the form of a rule, you'll understand it not as a rule, but by connecting it to examples that already exist in your head.
For instance, when sixth-graders learn that "singular subjects need singular verbs", that rule is incomprehensible by itself. But, once kids realize that the rule is just fancy language for the fact that "My dog has fleas" is right and "My dogs has fleas" is wrong, then it instantly makes sense.
In fact, the labels "singular" and "plural" aren't at all necessary, unless you are trying to communicate grammatical ideas to other people. In terms of understanding how the grammatical system works, they are irrelevant, and may even inhibit understanding rather than promote it.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron
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The perfect argument!lunarpower wrote:
I use analogies because the human brain is fundamentally wired for analogies/examples/experience, and not for rules.
Think about how you learn your first language, of which your knowledge is incredibly thorough. (Even if a professional linguist studies your language for years and years, (s)he will not approach anywhere near the level of competency you had in it when you were 11-12 yearsold.)
How many "rules" for your first language do you learn growing up? Zero. None. Just endless exposure to tons and tons of examples (from your parents, your friends, and whomever else).
Growing up, even if you see something stated in the form of a rule, you'll understand it not as a rule, but by connecting it to examples that already exist in your head.
For instance, when sixth-graders learn that "singular subjects need singular verbs", that rule is incomprehensible by itself. But, once kids realize that the rule is just fancy language for the fact that "My dog has fleas" is right and "My dogs has fleas" is wrong, then it instantly makes sense.
In fact, the labels "singular" and "plural" aren't at all necessary, unless you are trying to communicate grammatical ideas to other people. In terms of understanding how the grammatical system works, they are irrelevant, and may even inhibit understanding rather than promote it.
I now see why you constantly fight against rule memorization. Common sense, meanings (belong to natural world) go first, then people make up rules (belong to artificial world)
But dangers are there for using this powerful technique (analogy). I experienced this: One day I misused a duck's legs instead of a chicken legs, so I actually heard "cac cac" (the duck's voice) in the chicken.
I'm wondering something, not sure if it's relevant to ask. Could I apply analogy to sooner see patterns of math problems if I don't have enough pattern in my head because I had studied them little before? Or I need to have enough patterns in order to make right analogies, so no way is a shorter way?
( by "seeing patterns" I mean seeing similarities in different things in a group)