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12 Days of Christmas GMAT Competition 2025 - Day 2: If (3.7 * 10^a)

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rutikaoqw

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16 Dec 2025, 21:57

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Multiply both sides by 100
37 * 58 * 10^ a+b = 21.46 * 10^c
21.46 * 10^-2 * 10^a+b = 21.46 8 10^c
c= a+b-2

Gmat860sanskar

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16 Dec 2025, 22:09

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As we can see that 3.7 * 5.8 = 21.46

so let's assume that a = -1 ( to keep the values constant) ; b = -1 ; c = 0

Now check the option:

a + b + 2 - option B is the correct answer

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16 Dec 2025, 22:24

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(3.7*10^a)*(5.8*10^b)=3.7*5.8*10^a+b
=21.46*10^a+b
=0.2146*10^a+b+2
this is equal to 0.2146*10^c

from this c=a+b+2

yuvrajbhama

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16 Dec 2025, 22:39

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let a=1, b=2. 37*580= 21460 and to make it into 0.2146 c should be atleast 5 so option B makes it to 1+2+2=5

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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gmat147

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16 Dec 2025, 23:07

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Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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=> 3.7 * 10^a * 5.8 * 10^b = 0.2146 * 10^c
=> 21.46 * 10^(a+b) = 21.46 * 10^c * 10^-2
=> a+b = c-2
=> a+b-2 = c

asperioresfacere

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16 Dec 2025, 23:13

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3.7 x 5.8 = 21.46 , So now we have 21.46 x 10^a+b
We can write this as (0.2146x 10^2 )x 10^a+b
0.2146 x 10 ^2+a+b = 0.2146 x 10^c
Bases are same , Powers must be equal
2+a+b= c
Hence Option B is correct

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16 Dec 2025, 23:17

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To me, this makes most sense to do by assuming values for the variables. Also, the smaller the value, the easier the math. I also try to pick different values for each variable - as I've more often than not observed that picking the same values leads to multiple choices seeming valid, and wrong answers as a consequence.

For 3.7*10^a, I assumed a to be 0, which makes this 3.7*1 = 3.7. Simple.

For 5.8*10^b, I assumed a to be 1, which makes this 5.8*10 = 58.

Clearly, 58*3.7 will be around 210, and the LHS shows us 0.214. Each power of 10 this is multiplied with, will move the decimal one place to the right. We need that done thrice. So, 10*3 or 1,000 should be sufficient.

In other words, a = 0, b = 1, and c = 3. Great, we can start fitting these into the options.

A. c = a + b - 2 will become 3 = 0 + 1 - 2 = -1, hence wrong.

B. c = a + b + 2 will become 3 = 0 + 1 + 2 = 3. This could be the answer. But let's plug in the values to the other answers to be sure.

C. c = (a + b) / 2 will become 2 / 2 or 1, which is wrong.

D. c = ab - 2 will become 0 - 2, which is not 3.

E. c = ab + 2 will become 0 + 2, which is not 3.

So B would be the correct answers.

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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remdelectus

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16 Dec 2025, 23:19

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(3.7X5.8) X(10aX10B)
21.46 X 10a+b =0.2146x10c
21.46=0.2146x100
0.2146X10(2+a+b) =0.2146x10c
c=2+a+b
c=a+b+2

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16 Dec 2025, 23:25

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We can rewrite the equation as;

[(37 * 58)/100] * 10^(a+b) = [2146/10000] 8 10^(c)

37 * 58 / 2146 = 1

=> a+b = c-2
=> c = a+b+2 (B)

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16 Dec 2025, 23:28

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3.7*5.8 = 21.46 (do not need to calculate it, guess that 7*8 = 56, end with 6 and the answer choice reveals that it has an easy number)

21.46 x 10 ^ (a+b) = 21.46 x 10^(-2) * 10^c

eliminate 21.46, then

10^(a+b) = 10^(-2+c)

eliminate 10, then

a+b=c-2
c=a+b+2 (B)

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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bhnirush

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16 Dec 2025, 23:32

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Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Given,
(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c

Computing, 3.7 * 5.8 = 21.46

=> 21.46 * 10^a * 10^b = 21.46 * 10^(-2) * 10^c

Dividing by 21.46 on both sides,

And we know that X^y * X^z = X^(y+z)

=> 10^(a+b) = 10^(c-2)

Also when X^m = X^n => m = n,

=> a+b = c - 2
=> c = a + b - 2

Therefore, answer B) a + b - 2

HarishChaitanya

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16 Dec 2025, 23:49

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Multiplying 3.7 * 5.8 gives 21.46 which can be further deduced to 0.2146 * 10^2

Now the LHS term becomes 0.2146 * 10^( a+b+2)

When requested with RHS, C becomes a+b+2
Therefore answer is B

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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sanktmohanty123

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16 Dec 2025, 23:56

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The correct answer is option A

(3.7*10^a) * (5.8*10^b) = 0.2146 * 10^c
3.7*5.8 * 10^(a+b) = 0.2146 * 10^c
21.46 * 10^(a+b) = 0.2146 * 10^c
0.2146 * 10^(a+b+2) = 0.2146 * 10^c

=> c = a + b + 2

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17 Dec 2025, 00:25

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Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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On LHS, (3.7*10^a) x (5.8x10^b) = 21.46 * 10^(a+b)

On RHS, 0.2146 * 10^c = 21.46 * 10^(c-2)

Based on this, we can see that 10^(a+b) = 10^(c-2)

Equating the exponents, a+b = c-2

Therefore, c = a+b+2

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17 Dec 2025, 01:00

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If we calculate the values on the left hand side of the equation, we get 21.46*10*(a+b)

3.7*5.8 = 21.46
10^a*10^b = 10^(a+b)

If we now consider the RHS that value comes out to be 0.2146*10*c which can also be written as 21.46*10^-2*10^c = 21.46*10^(c-2)

On equating both the RHS & LHS,

10^(a+b) = 10^(c-2)
a+b=c-2
c=a+b+2

Therefore the answer is option B

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17 Dec 2025, 01:08

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3.7 * 5.8 = 21.46

21.46 * 10^(a+b) = 0.2146 * 10^c
21.46 * 10^(a+b) = 21.46 * 10^(c-2)
a+b = c-2
c = a+b+2

Ans. B

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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tanvi0915

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17 Dec 2025, 01:19

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I think the answer is B because 3.7 * 10^a*5.8*10^b = 21.46 * 10^(a+b) = 0.2146 * 10^2 * 10^(a+b) = 0.2146 * 10^(a+b+2) this is said to be equal to 0.2146 * 10 ^ c therefore since bases are equal we can see c in terms of a and b will be c = a+b+2

malvikasachdev124

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17 Dec 2025, 01:41

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3.7*5.8=21.46 (which can also be written as 0.2146 * 10^-2)

3.7*10^a * 5.8*10^b = 0.2146*10^c
3.7*5.8*10^a+b=21.46*10^c-2
a+b=c-2
a+b+2=c

ayaazansari97

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17 Dec 2025, 01:55

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Rewrite:
37 * 10^a-1 x 58x10^b-1 = 2146 x 10^c-4

37*58 = 2146 (Hint: the unit digit was matching on both the sides)

(a-1) + (b-1) = c-4
c = a+ b +2

Option B