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If a, b, and c represent distinct digits, what is the value of the two

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If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 21 Mar 2017, 03:49
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 21 Mar 2017, 10:49
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10



(1) b^2=c

if b =-2 , c= 4
if b= -3 , c=9
a could be 5 or 6
not suff

(2)again same as (1)
insuff


combining same as above
insuff

Ans E
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 21 Mar 2017, 22:00
rohit8865 wrote:
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10



(1) b^2=c

if b =-2 , c= 4
if b= -3 , c=9
a could be 5 or 6
not suff

(2)again same as (1)
insuff


combining same as above
insuff

Ans E


I believe that you are misinterpreting the question. a, b, and c represent digits, and ab, ba, and aca represent two two-digit numbers and a three-digit number. These are not products. Like, for instance, if a = 8 and b = 3, then ab would be 83, ba would be 38, etc.
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 21 Mar 2017, 23:58
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1.suff: 21 12 only combo acceptable as digits are different
2. insuff

answer A
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 22 Mar 2017, 01:02
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10


St 1: Nothing can be predicted. INSUFFICIENT

St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT

St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....

only 12*21 = 252

hence ab can be 12 or 21. INSUFFICIENT

Option E
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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ByjusGMATapp wrote:
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10


St 1: Nothing can be predicted. INSUFFICIENT

St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT

St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....

only 12*21 = 252

hence ab can be 12 or 21. INSUFFICIENT

Option E


ab can not be 12, only 21 because aca is 252
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 22 Mar 2017, 06:28
rt9 wrote:
ByjusGMATapp wrote:
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10


St 1: Nothing can be predicted. INSUFFICIENT

St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT

St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....

only 12*21 = 252

hence ab can be 12 or 21. INSUFFICIENT

Option E


ab can not be 12, only 21 because aca is 252


11 and 11 is another value
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If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 22 Mar 2017, 07:58
vivek2k70 wrote:
rt9 wrote:
ByjusGMATapp wrote:
St 1: Nothing can be predicted. INSUFFICIENT

St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT

St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....

only 12*21 = 252

hence ab can be 12 or 21. INSUFFICIENT

Option E


ab can not be 12, only 21 because aca is 252


11 and 11 is another value


It is mentioned in the stem that a, b, and c represent distinct digits.
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 22 Mar 2017, 09:25
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I am sure, you wanted to mention: If a, b, and C represent distinct digits
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10


We know a,b,c are different digits.

ab*ba = aca

So from the 2 digit multiplication process, first we will multiply a*b. As we get the unit digit number as a itself, means b = 1.

just plugging the numbers 21 & 12 gives 252, means a=2, b=1, c=5.

Also there is no other integer which gives mutiplication X1 * 1X = X_X
A- sufficient.
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Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 22 Mar 2017, 09:34
RMD007 wrote:
I am sure, you wanted to mention: If a, b, and C represent distinct digits
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10


We know a,b,c are different digits.

ab*ba = aca

So from the 2 digit multiplication process, first we will multiply a*b. As we get the unit digit number as a itself, means b = 1.

just plugging the numbers 21 & 12 gives 252, means a=2, b=1, c=5.

Also there is no other integer which gives mutiplication X1 * 1X = X_X
A- sufficient.


Sure. Edited. Thank you for noticing. +1.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 22 Mar 2017, 22:15
ByjusGMATapp wrote:
Bunuel wrote:
If a, b, and b represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10


St 1: Nothing can be predicted. INSUFFICIENT

St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT

St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....

only 12*21 = 252

hence ab can be 12 or 21. INSUFFICIENT

Option E



ByjusGMATapp plz elaborate the stat1 ,, according to me stat 1 is suff and 12,21 is the only combo tat fits in.. thanks
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If a, b, and c represent distinct digits, what is the value of the two [#permalink]

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New post 11 Jan 2018, 11:29
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Statement 1:
\(ab\) * \(ba\) = \(aca\)
=> \((10a+b)(10b+a)\) = \(100a + 10c + a\)
=> \(100ab + 10a^2 + 10b^2 + ab\) = \(100a + 10c + a\)
=> \(100ab + (a^2 + b^2)10 + ab\) = \(100a + 10c + a\)

now comparing units digit on both the sides
\(ab\)= a => \(a= 0\) OR \(b = 1\) => but a cannot be 0, if it were, then aca would be 2-digit number => b = 1

now comparing tens digit on both the sides
\(a^2 + b^2 = c\)
\(a^2 = c - b^2\)
\(a^2 = c - 1\)
\(a\) = \(\sqrt{c - 1}\)
only for c = 1, 2, 5, \(\sqrt{c - 1}\) yields integer
if c = 1, a = 0 (which is not possible)
if c = 2, a = 1 (but b is already 1) => not possible
so only c = 5, a = 2, possible
so number ab = 21 => sufficient

Statement 2: a * b < 10
lot of combinations ab = {14, 21, 24} not sufficient

(A)
If a, b, and c represent distinct digits, what is the value of the two   [#permalink] 11 Jan 2018, 11:29
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