For how many two digit positive numbers will tripling the tens digit give us a two digit number that is triple the original. (Contributed by: Srinivasan, Hyderabad)
A) None
B) 1
C) 2
D) 3
E) 4
GMAT Question of the Day: Number Theory
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D) 3
Range 10 … 99
soln => 10 … 1* 3 = 30 equals 30
11 … 1 * 3 = 31 not equals 33
Similarly for 20 and 30 but not forty onwards
Ans should be A.. none
If the number is ab then there is no possibility that 3a will give a number which is 3*ab.
For 10, lets say ab,
a=1, b=0 and hence 3a=3 whereas 3*ab=30 which does not equal 3.
Hi Maniranjan Kumar,
If the number is ab then there is no possibility that 3a will give a number which is 3*ab
take above line as>>>>>>
If the number is ab then there is possibility that (3a)b will give a number which is equal to 3*(ab)
VPat your answer is correct….
Hi GMAT Team ,
Could you explain the rationale behind VPat’s answer i ditn get it .
Also in your explanantion wat do u imply by take above line as >>>>>
Thanks
Vini
Ohhh >>>>>>> this imply nothing.
Dear Vini,
Just let us know at which point you are not able to understand, then we can focus on that step.
d
let the number be 10X + Y
tripling the ten digit number= 3X
now number is (3X)x10 +Y
the number becomes 3 times the original number 3(10X+y)
equating the above two
30X+Y= 30X +3Y
=> Y=0;
SO the numbers are 10,20,30
so answer is option “D”
any 2 digit number will be 10x + y
if we have a new number which is havng 3 times the 10′s digit this will be 30x + y
acc to the crriteria
30x + y = 3(10x +y)
i.e 30x + y = 30x + 3 y
which is possible only for y = 0
this all 2 digit numbers which are a multiple of 10 and which when multiplied by 3 are less than 100
which is 10, 20,30
Thus 3 –> D
Let’s say ab is two digit no.
now ab=10a+b
now if we triple the ten’s digit now the tripple of original no.
then (3a)=3*(ab)
here ab is two digit number which doesnt means a*b
but it means 10a+b
so
now 3a=3*(10a+b)
so 3a=30a+3b
-27a=3b
-9a=b
which means either a or b need to be negative and which does
not satisfy the condition(both a & b are positive)
so the answer is “None”
none
Its C … numbers are 10 , 20 and 30
of a number is xy then ..question stem says
3( 10x+ y) = 3(10X) + y
it gives y =0
now.. numbers could be 10 , 20 …till 100 but ..from 40 onwards ..
if X> 3 . then 3x will not be one digit and hence number will not be two digits ..
you cannot count 10,20,30 because 0 is not a positive digit number
Therefore, answer a is right
i feel d) is the answer…
10,20,30
Ans is A.
Question should go for sentence correction
well the numbers falling for this Q are 10, 20 and 30 and hence some friends said ans D. Now, tripling the ten digit of these numbers are not going to give 2 digit numbers
1*3 = 3, not a 2 digit number
2*3 = 6, not a 2 digit number
3*3 = 9, not a 2 digit number
Hence D cannot be the correct answer.
only 3 numbers – 10,20 and 30
Answer should be “D” after clarification from the MOderator.
Good comment by Nishesh
D is the right answer
ab(10-99) => 10a+b
30a+b = 3*(10a+ b) where ab = 0
00 ain’t possible, so 10,20,30
The number can be thrice only when it end s with a 0
bcos when its 1 it ends with 1x 3 =3
and so on with other numbers
now the tens digit has to be so … that when it is tripled it has to be below 10 so that the total number remains below 100 i.e., 2 digit number
tens digit can thats y be either 1 , 2 or 3 …. above 3 it triples to more than 10 bcoming 3 digit number
so the three numbers are 10, 20 n 30
@nishesh
absolutely correct dude
it kept me confused for a lot of time.. the sentence should be better framed
Sorry but I would go with A since this question doesn’t even make any sense to me. Tens = 10,20,30 right?
How do you ever triple a tens and get an answer that is two digits and not three? I am so confused.
10, 20 and 30
Answer is D) 3
Numbers are 10, 20 and 30.
ummmm…i dint really go that far..all i knew is that I need to have 0 in my units so that trpling it will remain the same…and tripling the tens number would give the triple of the 2 digit number..
was i wrong to come to a quick conclusion this way???
I will go with option D)3
D.
10 20 30
for 40: 40*3= 120 which is 3 digit number
thus only for 3 numbers does the condition hold true
According to the condition, there is only one digit possible
at unit place..i.e.0…so we have fix unit’s place
Now starting wid the smallest 2 digit no.10..(it fulfils the condition)
and thus moving forward, i.g. by putting 2, 3,4….at 10s digit place, we get 3 such nos..10,20 n 30..
Hence ans -D
The answer is D. I infer from the question that we should take the face value of the digit in the tens place (which is the digit itself) and then multiply by 3, rather than taking the place value (i.e. tens) I hope I have not added to the confusion.
D…
D.
D