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

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Harsha_VS

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17 Dec 2025, 02:42

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LHS: Multiplying 3.7 x 5.8 yields 21.46 and 10^a x 10^b yields 10^(a+b) [Formula: a^p x a^q = a^(p+q)]
RHS: 0.2146 x 10^c, which can be written as 21.26 x 10^(c-2)
Equating both LHS and RHS, we will be left with
a+b=c-2
a+b+2=c

kapoora10

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17 Dec 2025, 02:44

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LHS = (3.7*10^a) x (5,8*10^b) => 3.7*5.8 X (10^(a+b)) => 21.46 x (10^(a+b)) => 0.2146 x (10^(a+b+2)) ... 1
RHS => 0.2146*10^c ... 2

=> Using 1 and 2 - a+b+2 = c

Correct Answer => B

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17 Dec 2025, 03:03

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Answer: B

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

$(37*10^(a-1))(58*10^(b-1))= 2146*10^(c-4)$

Thus,
$37*58*10^(a+b-2) = 2146* 10^(c-4)$
a+b-2= c-4
a=b+2=c

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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hershehy

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17 Dec 2025, 03:32

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IMO B
A little look at Question would tell us that the product of 3.7 * 5.8 would result in >20 and <24. then by unit digit we can see 6. So the product has to be 21.46.

now we have; 21.46 * 10^a * 10^b= 0.2146 * 10^c
we can rewrite 21.46 = 0.2146 * 10^2, therefore, 0.2146*10^(a+b+2)= 0.2146 * 10^c
dividing both sides with 0.2146, we have
c= a+b+2

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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Saks116

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17 Dec 2025, 03:39

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(37/10)*10^a*(58*/10)*10^B = 2146/10000*10^C
= 37*10^(a-1)*58*10^(b-1) = 2146*10^(c-4)
= 2146*10^((a-1) +(b-1)) = 2146*10^(c-4)
= a-1 + b-1 = c-4
= a+b+2 = c

B

Reon

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17 Dec 2025, 03:59

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(3.7*10^a)*(5.8*10^b)=0.2146*10^c
37*10^(-1)*(10^a)*58*10^(-1)*(10^b)=2146*10^(-4)*10^c
2146*10^(-1-1)*10^(a+b) = 2146*10^(c-4)
10^(a+b-2) = 10^(c-4)
Comparing both sides
a+b-2=c-4
c=a+b-2+4
c=a+b+2

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17 Dec 2025, 04:19

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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
=> 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

Comparing both sides, we get c = a+b+2

Option B

Vaidehii

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17 Dec 2025, 04:22

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So->
21.46 X 10^a+b=0.2146X10^c
2.146X10^a+b+1=2.146X10^c-1
Now take power
a+b+1=c-1
a+b+2=c

Vamikaaa

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17 Dec 2025, 04:28

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3.7*5.8 = 21.46
to get to RHS, consider that as 0.2146 * 10^2

Thus, LHS = 0.2146 * 10^2 * 10^a * 10^b = 0.2146 * 10^(a+b+2)

hence, c = a+b+2

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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meenumaria

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17 Dec 2025, 05:40

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IMO answer B is correct
3.7*10^a x 5.8*10^b =0.2146*10^c
=>3.7*5.8*10^a+b = 21.46*10^-2 *10^c
==>21.46*10^a+b= 21.46*10^c-2
cancel 21.46 both sides
10^a+b = 10^c-2
a+b=c-2
c=a+b+2

Sujithz001

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17 Dec 2025, 05:57

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Qn: What is c in terms of a and b?

37 * 58 = 2146, great. Now, it's a matter of adjusting decimals.

Then, 3.7 * 5.8 = 21.46, cool we need to move 2 decimals forward, so c should be -2.

Since both terms are in multiplication, exponents will be added, thus a + b = -2

Hence, answer is a + b + 2.

asdf611111

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17 Dec 2025, 05:59

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Removing decimals and solving the equation will give you this
formula used a^m * a^n = a ^ m+n
and 1/a^m = a^ - m
accoridng to question equation will look like this
(37 * 10 ^(a-1))(58 * 10 ^ (b-1) ) = 2146 * 10 ^ (c-4)
now 37 *58 = 2146 that gets cancelled out on lhs and rhs and you will have
a - 1 + b -1 = c-4
a+ b+ 2 =c

atenim

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17 Dec 2025, 06:18

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multiply lhs and you wilget 21.46, rhs is 0.2146 so take power of 2 from 10, c-2 will be rhs and lhs will be a+b, i.e c=a+b+2. Option 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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Mardee

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17 Dec 2025, 07:05

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We have been given,
(3.7*10^a)(5.8*10^b) = 0.2146 * 10^c

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

From what we have, we can conclude that,
a+b+2 = c

B. a+b+2

sureshkumark

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17 Dec 2025, 07:09

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21.46*10^a*10^b=21.46*10^c-2 => a+b=c-2=>c=a+b+2... Therefore , the answer is choice B

asmitatiwari26

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17 Dec 2025, 07:35

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First Multiply the number 3.7*5.8 = 21.46
When power of 10 are multiplied exponents get added,
(3.7*10^a)*(5.8*10^b) = 21.46 * 10^(a+b) ----(1)
Now inorder to compare both side we need to rewrite the above in same form as 0.2146 by moving two decimals to the left and to keep the value same we need to multiple bu 10^2 which will give the equation as:
21.46 = 0.2146*10^2
how if we put the value of 21.46 in equation 1 we get ,
0.1246*10^2 * 10^(a+b)
Combining the power of 10 again we get, 0.1246*10^(a+b+2) --(This is now our left side equation)
Comparing the left side with right side we get value of c = a+b+2

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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haldersujoy

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17 Dec 2025, 07:46

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Given,

(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c
=> (3.7 * 5.8) * (10^a * 10^b) = 0.2146 * 10^c
=> 0.2146 * 10^2 * 10^a * 10^b = 0.2146 * 10^c
=> 10^a+b+2 = 10^c
=> c = a+b+2
OA: 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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DhanyaAbhirami

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17 Dec 2025, 08:01

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RHS is 2146 x 10 ^(a+b-2) = 0.2146 X an^(a+b-2+4)
c = a+b+2

Veerenk

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18 Dec 2025, 18:05

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

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

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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