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May 0608:30 AM PDT
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In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory....- May 08
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30 May 2023, 10:56
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
30% (02:34) correct
70%
(02:59)
wrong
based on 44
sessions
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Not Attempted Yet
P and Q are two two-digit numbersTheir product equals the product of the numbers obtained on reversing them. None of the digits in P or Q is equal to the other digit in it or any digit in the other number. The product of tens digits of the two numbers' is a composite single digit number. How many ordered pairs (P, Q) satisfy these conditions?
(A) 8
(B) 16
(C) 12
(D) 4
(E) 9
Posted from my mobile device
(A) 8
(B) 16
(C) 12
(D) 4
(E) 9
Posted from my mobile device
31 May 2023, 13:23
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Arick
P = xy ⇒ 10x + y
Q = pq ⇒ 10p + q
The reverse numbers are
Reverse(P) = yx = 10y + x
Reverse(Q) = qp = 10q + p
This question can be solved using a two-step process -
- Identify the relationship between x, y, p, and q.
- Identify the pairs of values that satisfy that relationship
Step 1: Identify the relationship between x, y, p, and q.
Given: Their product equals the product of the numbers obtained on reversing them
\((10x + y) (10p+q) = (10q + p)(10y +x)\)
\(100xp + 10xq + 10yq + yq= 100qy + 10qx + 10py + px\)
\(99(xp - yq) = 0\)
\(x*p =y*q \)
Step 2: Identify the pairs of values that satisfy that relationship
Constriants:
- None of the digits in P or Q is equal to the other digit in it or any digit in the other number
- The product of tens digits of the two numbers' is a composite single digit number
Inferences:
- None of the digits in P or Q is equal to the other digit in it or any digit in the other number
\(x \neq y \neq p \neq q\) - The product of tens digits of the two numbers' is a composite single digit number
\(x *p\) is composite number
If x = 1, p \(\neq\) prime and vice-versa
Let's try to understand the given conditions a bit better, let's say x = 2 and p = 3
2 * 3 = y * q
So (y,q) can be (1,6) or (6,1) but not (2,3) or (3,2). So for one combination of (x,p) we can have four possible values
(x,p) = (2,3)
- (y,p) = (6,1)
xy = 26 | pq = 31 - (y,p) = (1,6)
xy = 21 | pq = 36
(x,p) = (3,2)
- (y,p) = (6,1)
xy = 36 | pq = 21 - (y,p) = (1,6)
xy = 31 | pq = 26
Possible values of (x,p) = (1,6), (1,8), (2,3), and (4,2).
Total possible combinations = 4 * 4 =16
Option B
P.S. - This is not a GMAT Style question.
31 May 2023, 20:46
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Arick
Let's say the 2 digit n.o are in the for of ab cd
So value of the numbers is 10a+b, 10c+d.
If we solve the below equation i.e, (10a+b)(10c+d) = (10b+a)(10d+c)
We will get ac = bd.
We know that ac is a composite single digit. So possible values are 4,6,8,9
a*c = b*d = {4,6,8,9}
All 4 are distinct.
So 4,9 are not possible.
a*c=6 or 8 .
2*2*2*2 possibilities.
16
IMO B
